Occupants of offices on the east side of the Old Executive Office Building have become accustomed to looking out their windows and seeing the bulky, rumpled figure of Bert Lance scooting across the street to the White House.

Late in the afternoon, they know, it's likely he's on his way to play tennis with the President. Around noon, especially on Thursday, chances are he's going to join Jimmy Carter for lunch off trays in the Oval Office.

If Lance is with a group, it's probable that the director of the Office of Management and Budget is headed for a budget briefing with the President.

But whatever the occasion, the frequency of Lance's trips across West Executive Avenue is evidence of the large and expanding role the 46-year-old Calhoun, Ga., banker-politician plays in this administration.

Hamilton Jordan, Carter's top White House assistant, says the President "looks on Bert almost as an extension of himself," and others in the inner circle testify to the closeness of the Carter-Lance relationship.

Not everyone in the administration, of course, regards their intimacy as good news. There are persistent complaints from within the Office of Management and Budget professional cadres that Lance is sloughing off the detail work of his own job in favor of trouble-shooting and public relations for the President.

Some of Carter's political advisers think the budget chief's preeminent influence on the President has given the administration a more conservative tilt than is healthy. "Carter will be better off when Bert Lance loses his first inside battle," said one of those advisers. "The lean now is all in one direction."

His judgment was based on Latice's prevailing over the reported opposition of Jordan, Vice President Mondale, Council of Economic Advisers Chairman Charles L. Schultze and Domestic Affairs Assistant to the President Stuart Eizenstat on a series of economic policy issues. Lance is credited with success in the interanl debates and decisions that led to cancellation of the proposed income income tax rebate,restriction of minimum wage increases and farm price support boosts and opposition to various water projects.

He is identified as the leader of those urging the President to take a hard-line toward Congressional boosts in appropriations for health, education and welfare programs.

In every instance, Lance has been fulfilling the budget director's traditional role of questioning the wisdom of measures that will cost the government money, reduce its income and add to its deficits - thus playing his part in Carter's drive to achieve a balanced budget by the end of his first term.

Lance himself said in an interview last week that there is "nothing at all" unusual about the influence he wields. "I'm not conscious of anything where I'm involved in a way that is out of character for the man in my job," he said.

The budget directorship is an inherently powerful job, giving its occupant license and a duty to second-guess every agency head, in the course of the containing process of budget review.

During the Nixon years, the budget chief was also given responsibility for improving the management of government operations. Two of Nixon's OMB heads signaled their broadened influence by taking offices in the West Wing of the White House, as well as in the traditional budget headquarters in the neighboring Old Executive Office Building.

But when Gerald R. Ford came to the White House, he was urged by his advisers to restore a more traditional role for the budget chief. James T. Lynn, who had been one of the Nixon Cabinet members, complaining about OMB, stayed on his side of the street when he took over OMB for Ford. Lynn contented himself with mastering the budget process and pushing forward OMB's sluggish management-improvement efforts.

A variety of circumstances have encouraged - or some would say, compelled - Lance to adopt a more expansionary view of his responsibilities.

Uniquely among the budget directors of the past 30 years, Lance came to the position already a personal and political intimate of the President.

He had backed Carter for governor of Georgia, became commissioner of highways and political troubleshooter in the Carter administration and, in turn, was Carter's choice as a successor in the statehouse.

That Carter plan was frustrated when Lance lost in the 1974 Democratic gubernatorial primary. But, as a private banker, Lance financed an expansion of Carter's peanut-processing business and floated loans that helped the fledgling Carter presidential campaign solve some of its cash-flow problems.

When Carter introduced him to the country last Dec. 3 as his choice to head OMB, he noted that Lance had been his partner in the reorganization of the Georgia government.

With Carter's encouragement, Lance has rooted the President's cherished federal reorganization effort in OMB, thus gaining further leverage in the bureaucratic struggle.

As one White House staff member comments, "At the same time that we're arguing policy with Lance on the spending issues, we're busy justifying our very existence to his people."

The reference was to the OMB study of the Executive Office of the President - the White House and its satellite agencies - now nearing completion. Lance is preparing recommendations for submission to Carter this month on the size and shape of the reorganized executive office, a prospect which one outsider with great access to the White House says "is terrorizing the people" in offices that maybe targeted for reduction.

In addition to managing the reorganization effort, Lance has taken over another top-priority Carter project, the introduction of zero-base budgeting.

Last week, he started presenting the mid-year budget review to the President, a process that will consume over 24 hours of presidential time by its completion and will set the guidelines for the creation of the fiscal 1979 budget, the first for which the Carter administration will bear full responsibility.

Beyond these formal duties, Lance functions as a sounding-board for the President on almost any personal, political or governmental question on the President's mind. Last weekend, on vacation, they walked the beach on St. Simon's Island for two hours. One associate says that there have been occasions on the White House tennis court when the two became so engrossed in conversation that the game was forgotten.

To some observers, Carter's style of management has created unusual opportunities for the budget director to play a policy role greater than his predecessors enjoyed.

Carter has declined to designate a chief of staff within the White House. Jordan, who comes closest to filling that role, so far has shunned getting deeply involved in a wide range of issues.

In the view of some insiders, that has left the job of policy coordination increasingly in the hands of Lance, whose budget duties take him into every question, from the B-1 bomber to the Agency for Consumer Protection.

Also, these observers note, Carter has issued strict orders to his own White House assistants against "interference" in the operations of the departments and agencies. The inhibitions on Eizenstat's domestic policy staff, particularly, have made Lance's budget assistants the chief contact point between the bureaucracy and the White House.

Given the enormous range of his influence, some of Lance's critics within the administration question whether the OMB director is spending enough time at his own desk to master the detail of his job.

No one accuses him of shirking at his labors. He is in the office most mornings before 8 a.m., and when he leaves for dinner at his Georgetown home, he is lugging a heavy sack of night reading.

Most weekends, however, Lance heads home to Georgia. And even during office hours, only a fraction of Lance's time is spent on the humdrum work of management and budget.

He has become the businest speechmaker in the administration and the most accessible press source, returning all reporters' calls personally.

The past week's schedule shows twice as many appointments with outsiders - reporters, businessmen, members of Congress, visiting Georgians - as with OMB staff members.

While lavish in his praise of the OMB career bureaucrats, Lance has added a new layer of "executive associate directors" between himself and the career people. His deputy director, James T. McIntyre Jr., a former colleague in Carter's Georgia administration, runs two of the three weekly senior staff meetings and, says one OMB professional "really presides at the third meeting, even when Lance is in attendance."

Lance and McIntyre both say that the delegation s of authority has not removed Lance from effective control of his own agency. But McIntyre concedes that the "unsettled" character of Lance's own schedule has made it impractical for them even to fix a standard time for a daily meeting.

But if there are misgivings within OMB about Lance's time priorities, there are no evidences of dissatisfaction on the President's part.

An aide says Lance's wide-ranging contacts in the business, political, congressional and journalistic worlds are a valuable resource to a President who complains of the time and security restraints that prevent him from circulating as freely himself.

As for the charge that he is too much of a conservative force, Lance himself seems to be taking steps to change the image.

When an assistant pointed out recently that he had talked to over 50 business, banking and investment groups since becoming budget director, but not a single union convention. Lance initiated a one-hour meeting with AFL-CIO secretary-treasurer Lane Kirkland.

In recent interviews, he has begun stressing that he and the President are seeking a balanced budget "in order to make possible the social programs we all want."

This week, he made his first public criticism of those favorite liberal bugaboos - Arthur Burns, the Federal Reserve Board and high interest rates.

His intra-administration critics think this is just a bit of political public relations on Lance's part. But whatever his image, no one - friend or foe - doubts Lance's influence. His clout is where it counts - in the Oval Office. And the man who works likes Lance a lot.