Secretary of State Shultz has given himself a stern challenge by declaring that he favors no approach to Mideast peace but the Camp David framework. On the one hand, he will have to take such steps as assigning high-level negotiatiors to provide an impetus that the Reagan administration has not given so far. On the other, he will have to be flexible enough to consider other approaches if full US commitment fails to bring results.

The immediate question, of course, is peace in Lebanon. But this is part and parcel of longer-range security in the region. The connection has been highlighted in recent days by all the revived attention bestowed on the United Nations Security Council's Resolution 242 of 1967 - the basis for peace ''between Israel and its neighbors'' enshrined in the Camp David framework.

Secretary Shultz's well-known mettle would be reaffirmed by restoring this resolution to its promising role instead of the ''Catch-242'' it threatens to become. Among current paradoxes is the stress placed on the Palestine Liberation Organization accepting 242 if it wants diplomatic recognition - while Israel, which has always accepted 242, is seen as violating it with expansionist policies in occupied territories from which 242 requires it to withdraw. To which Israel says Camp David refers to 242 ''in all its parts,'' including references to security and independence as well as territorial withdrawals.

Part of the controversy involves 242's failure to refer to the Palestinians except in calling for ''a just settlement of the refugee problem.'' Camp David spells out that the ''legitimate rights'' and ''just requirements'' of the Palestinian people must be recognized.

Now trial balloons are bumping into each other with reports that PLO officials are seeking ways to gain US recognition by acknowledging 242 as a basis for negotiation. They might want a revision or an accompanying declaration recognizing Palestinian rights to self-determination. They might repeal PLO policy on eliminating Israel by acknowledging Israel's right to exist behind ''secure and recognized boundaries,'' to use the language 242 applies to all states in the area.

No doubt only an announcement by Yasser Arafat himself would bring such a balloon down to solid earth. He must calculate whether the PLO will ever have a more propitious moment to play this one-time-only card. Right now, ironically, the Israeli invasion of Lebanon seems to have given the beleaguered PLO new diplomatic leverage.

And right now is an occasion for Mr. Shultz's repute as a negotiator to be confirmed in his new post. Through imbuing his departmental and administration colleagues with a fresh spirit of fairness and conciliation - the spirit that underlay Camp David - he might be able to elicit it from the contending parties as well.

Why not a Sadat-type gesture from Arafat? Why not an Israeli response?

Cynics have many answers. Mr. Shultz is not a cynic.

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