The Carter administration's strategy for winning the necessary two-thirds Senate vote for the Panama Canal treaties emerged more clearly yesterday, and there were preliminary indications that the strategy was working.

Four officially "undecided" Democratic senators who meet with Vice President Mondale and other administration officials Thursday had lunch together yesterday and apparently made progress toward an agreed set of tactics that could end with all of them voting for the treaties.

This would involve one key reservation to the first treaty guaranteeing the canal's neutrality, and the elimination of one article - in fact or in effect - from the second treaty on the turnover of the canal to Panama. The administration has indicated to the senators that it could live with the changes they propose.

If these changes are adopted and the four Senators vote for final passage (along with a fifth like-minded colleague who could not attend yesterday's luncheon), the best available head counts suggest that the treaties will get 67 to 70 votes. If all 100 senators vote, 67 will be needed for final approval.

The public sign of progress toward this arrangement yesterday was a statement from both Georgia senators, Sam Nunn and Herman E. Talmadge, announcing that they would press for two changes.

The first would allow the United States to base troops in Panama after the year 2000 (when Panama would take over the canal) provided the nations agreed jointly on such basing. The second would eliminate the existing prohibition of U.S. negotiations with other Central American countries on possible construction of a new Atlantic-Pacific canal.

Nunn told reporters that, if adopted, these changes would make it much easier for him to vote for final passage. He stopped short of a firm commitment to vote yes, however,.

Besides the Georgians, the other senators in this group are Russell B. Long (D-La.), Dennis DeConcini (D-Ariz.) and Wendell Ford (D-Ky.).Long and DeConcini took part in yesterday's meeting, informed sources said.

In floor action yesterday the Senate overwhelmingly approved the first of two "leadership amendments" to the neutrality treaty. Both amendments have already been accepted by the Carter administration and the government of Panama.

The changes approved by 84-to-5 yesterday incorporates language setting out explicity the U.S. right to act to defend the canal's neutrality after 2000 if it is threatened.

This language and that of the second leadership amendment that will be voted on next week come from a joint statement issued last October by President Carter and Gen. Omar Torrijos, Panama's "maximum chief."

This was the first change approved during the four-week-old debate on the treaties. The Senate also voted down several more opponents' amendments yesterday.

President Carter met yesterday with three more undecided senators, Richard Schweiker (R-Pa.), Edward Brooke (R-Mass.) and Paul Hatfield (D-Mont.). None of the three changed their public positions after the meetings.

Schweiker, in an interview yesterday in which he listed reasons to vote both for and against the treaties, said it might not be a calamity if the first treaty is rejected when it is voted on Thursday, forcing the administration to reopen negotiations with Panamanians to incorporate changes that concern many senators.

But he refused to say how he will vote.