An Equal Rights Amendment lobbyist, an Alexandrian who claims it's time for his city to be represented and a high school teacher backed by organized labor are in a tight race for the Democratic nomination to the Northern Virginia floater seat in the House of Delegates.

The seat is up for grabs this year because Ira Lechner, its current occupant and a Democrat from Arlington, is running for lietenant governor. Arlingtonians have held the seat since it was established in 1971. The floater delegate represents both Arlington County and Alexandria.

Democratic party leaders in Arlington and Alexandria say the race between the three candidates - Elise B. Heinz, James McCaskill, and Robert L. Montague III - is wide open, with no front runner.

"I see ways where any one of the three of these people can win," said Jim Gondles, head of the Arlington County Democratic organization. "Elsie will get the feminists and pro-ERA vote. McCaskill will get organized labor and the teachers. Montague may be sitting in the saddle right now because he's from Alexandria and he may get Alexandrians united behind him."

The winter of the June 14 Democratic primary will face Republican Thomas G. Shfran in the November general election. Shafran, a realtor from Arlington, was nominated by the Republicans last week in a district convention in Arlington.

Heinz, a 42-year-old Arlington attorney, noted that "Arlington and Alexandria have nothing politically in common except this seat."

Heinz is a cum laude graduate of Harvard Law School who caught the political "bug" while lobbying for ERA in Richmond.

If elected, Heinz said she would be the first woman lawyer to serve in the House of Delegates. She said she would like to serve on the Courts of Justice Committee in order to help reorganize Virginia's court system and overhaul the sex crime statutes.

In addition, Heinz said the state needs to provide some kind of security for the full-time homemaker, "something resembling a community property concept." She would also continue to work for the passage of the ERA.

Heinz said she has been endorsed by the Virginia Women's Political Caucus and National Organization for Women (NOW) chapters.

McCaskill, 40, is an Arlington apartment resident and teachers government and psychology at Wakefield High School in Arlington. He was an unsuccessful candidate for the Arlington County Board in 1975.

McCaskill, a past president of the Arlington Education Association, has been endorsed by the Greater Washington and the Virginia AFL-CIO Committees on Political Education and by several education associations.

MCCaskill favors setting up a legislative budget office similar to the Congressional Budget Office. The way the state legislature now handles the budget is a "fiasco," he said. He supports the state beginning zero-based budgeting.

McCaskill said he wants to serve on House committees dealing with education, labor and conservation. He would push for tenants rights and for full funding of education, he said.

Montague, 41, is an Alexandria attorney and a former assistant attorney general in Kentucky. He ran unsuccessfully for the Alexandria-Fairfax floater seat in 1965 and for the Alexandria City Council in 1973.

Montague, considered most conservative of the three, is interested in issues dealing with conservation and historic preservation and has served on local commissions dealing with these issues. He would like to see solar energy used for space heat in public buildings, legislation to control throw-away beverage containers and tax incentives to encourage use of more fuel-efficient automobiles.

All these candidates support the ERA. Montague, however, said he is not certain whether he would vote to discharge it from committee, where it has remained bottled during past sessions.

The candidates' stands on other issues:

Collective bargaining for public, employees - McCaskill supports it with no limitations, but added that school boards need "certain authority" with boards need "certain authority" with those limitations worked out locally. Heinz supports collective bargaining, but said a no-strike provision would be "politically essential - it would be hard enough to pass such a bill even with it." Montague says he is "open minded" about public employees collective bargaining, but expressed concerns that it could interrupt public services and create and adversary relationship between state and local goverment and their employees.

A proposed Martin Luther King day - All three support some sort of commemoration. (The governor vetoed a bill last session that would have set up a day in King's honor.)

Judgeships and taxes - All three said they would support the creation of a judicial nomination commission, and all feel local jurisdictions should be given tax alternatives to relieve the overburdened property tax.

McCaskill estimated that he will spend between $3,000 and $4,000 on his primary campaign. Montague said he expects to spend about $5,000 and Heinz said she may spend $5,000 and $10,000.

The campaigning has been mainly door-to-door. At least one of the candidates has found that some voters aren't interested in energy, taxes and court reorganization.

One of Montague's precinct chairwomen who was campaigning in Fairlington Village recently was confronted by a resident with just one question about her candidate: "Does he play tennis?"