The Senate headed home yesterday for what will amount to a full week's recess for most members, despite all that stiff-upper-lip talk last month about restricting its lincoln and Washington birthday leavetaking to two days.

But it did manage first to make a partial breakthrough in its two-year-old snarl over the Alaska lands bill late Thursday, even though a complicated agreement setting forth terms for consideration of the measure stipulates that it won't come up until after July 4.

Whether this will be enough to satisfy the Carter administration, which is pressing for passage of the bill this year, was unclear, however. An aide to Interior Secretary Cecil D. Andrus said Andrus plans to urge President Carter to put more Alaska lands under 20-year protection, a process begun in 1978 in response to congressional paralysis on the issue.

Andrus had said he would act independently to protect 54 million acres unless the Senate made satisfactory progress by March 1.

A Senate Energy Committee bill favored by the state would set aside 102 million acres of Alaska as parks, refuges and other protected areas. A substitute, favored by enviromentalists, would set aside 125 million acres and designate twice as much of the total as development-free wilderness. The substitute is closer to a bill passed by the House last year.

The July 4 date apparently satisfied Sen. Mike Gravel (D-Alaska), who until Thursday had succeeded in keeping the bill off the floor with filibuster threats.

The Senate will meet Monday and Thursday in pro forma sessions, which few senators are expected to attend. The House is scheduled to take off next Thursday and Friday and the following Monday.