The Cambridge School Committee early Thursday morning unanimously adopted an "educationally sound" $36.7-million budget for the 1981-2 school year, which will still force the committee to lay off 138 tenured teachers and administrators because of funds lost under Proposition 2 1 2.

Next year's budget will allow the committee to keep some of the 274 teachers that Superintendent of Schools William C. Lannon originally said would have to be laid off but it is still $2.6 million below the current budget.

The Cambridge City Council must approve the school committee's budget, which is $1.6 million above the $35.1 million ceiling city manager James L. Sullivan set for the committee on its 1981-82 spending.

If the committee does not get an additional $1.6 million in anticipated funds, it will be forced to lay off an additional 40 teachers next fall under the $35.1-million limit set by Sullivan.

Sullivan was not available for comment yesterday, but City Councilor David A. Sullivan said yesterday that the school committee budget would create "a real problem for the city manager," who has to decide whether to pass the budget on to the city council.

Councilor Sullivan said that if the school budget were passed on to the council, "fighting" between different groups on the council would be "inevitable."

The school committee also set up guidelines for Lannon to follow if the budget had to be reduced further in the fall.

Cambridge Mayor Francis H. Duchay '55 said yesterday the school committee did its best to "come up with a budget we felt was needed" for quality public education. He added that he thought it was only "a question of time" before the state legislature acted to give Massachusetts cities and towns the money they need.