THE MYSTERY deepens over the friction between Israeli soldiers and American peacekeepers in Lebanon. Earlier incidents, and a consequent mutual resolve to put them to an end, have been followed by American allegations--and Israeli denials--of new tensions. It is a dismaying sequence.

Frankly, it is very difficult to believe that the Marine commandant, Gen. Robert H. Barrow, was inventing the events of which he complained in a letter that the Pentagon made public the other day. He said Israeli troops had put Marine and Army officers serving in Lebanon in "life-threatening situations . . . timed, orchestrated and executed for obtuse Israeli political purposes." Others have suggested that the Israelis wish to discredit American and, by extension, other foreign peacekeepers in order to strengthen the justification for leaving Israeli troops indefinitely on Lebanese soil to ensure Israeli border security. If this is so, it is completely objectionable.

It had seemed evident after the earlier incidents that Israelis and Americans alike wished to end this unseemly trouble between allies. Certain new arrangements were made on the ground to diminish the possibility of further misunderstandings. The departure of Ariel Sharon as defense minister, and his replacement by Moshe Arens, who appeared eager to turn a page in Israeli defense dealings with the Pentagon, seemed helpful in this regard. But not long afterward, Gen. Barrow now reports, the trouble began anew.

The United States seems not to have assented, as the other members of the multinational force in Lebanon have, to establishment of liaison offices at the field level of the military forces in Lebanon. The Israelis have their own dark suspicions as to why the Pentagon has not followed the pattern employed by the other countries. Would not liaison offices help? It is not clear just what changes in attitude or procedure need to be made, and by whom, in order to set matters straight. It is totally clear, however, that these frictions cannot be allowed to go on.