The US role in a lasting Mideast peace; A case for placing strings on future American aid to Israel; The United States in the Middle East: Interests and Obstacles, by Seth P. Tillman. Bloomington, Ind.: Indiana University Press. 333 pp. $22.50.

For anyone who is puzzling over what the United States should do next in the Middle East, following the PLO exit from Beirut, this should prove to be a useful book.

Don't expect dramatic disclosures of the inside story or brilliant new insights (perhaps there are no brilliant new insights to be had in this much-studied area). This is a dispassionate, well-documented history and analysis of American policy toward the Arab-Israeli conflict, which ends with recommendations for the future.

For those who are new to the subject, the book might be a good starting point. But to some friends of Israel, the book will be disturbing, because Tillman believes in the feasibility of a Palestinian state, to be built on the West Bank of the Jordan and in Gaza, as part of a comprehensive Middle East peace. To most Israelis, apparently, the idea is unthinkable.

Tillman tackles head-on, but in a scholarly way, the greatest Israeli, American, and Arab fears; brings out of the shadows the irrationalities that lie behind those fears; and then looks ahead.

The weakness in the book may be that events have moved so rapidly in recent months that the author could not possibly have taken into account the latest Israeli drive into Lebanon, the PLO evacuation, the Iranian attack on Iraq, and the oil glut. But with the Reagan administration and a new secretary of state now moving to deal more forcefully with the Palestinian issue, most of what Tillman has to say seems relevant to this very moment.

For busy people, the book's chapters can be read as separate essays, worthwhile in themselves. For example, for those who know a great deal about Israel but little about the Palestine Liberation Organization, the chapter on the Palestinians would be worth reading in and of itself and ahead of the chapter on Israel.

The book can also be read at several levels: It offers a refresher course in Middle East history, with the emphasis, of course, on the Arab-Israeli conflict - and on the longstanding ambiguities in American proposals aimed at resolving that conflict. It is a primer on vital American interests in the region. And it gives one of the best descriptions I've seen of the so-called Israeli lobby in the United States, an often misunderstood phenomenon. As Tillman points out, Israel's sympathizers in this country are so widespread and well placed that the Israelis have no need of hired American agents or lobbyists. The Israelis and their friends in the US know the American rules, and play the game harder than anyone else.

Tillman knows what he is talking about when it comes to the ''lobby.'' Now an adjunct professor of international relations at Georgetown University, he served as a member of the Senate Foreign Relations Committee staff when J. W. Fullbright headed that key committee.

Tillman supports what he describes as a consensus among moderates both at home and abroad on what to do to achieve an equitable settlement of the Arab-Israeli conflict. The key elements are: Israeli withdrawal to the borders of 1967, with minor variations in Israel's favor for purposes of defense; and Palestinian self-determination on the West Bank and in Gaza, conditional upon explicit, official Palestinian recognition of the permanence and legitimacy of Israel. There would be some form of Arab sovereignty over the Muslim holy places in Jerusalem, with unimpeded access thereto, demilitarized zones around all of Israel's borders, an end to all hostile actions against Israel, and the initiation by stages of normal relations between Israel and the Arab states.

All of this should be supplemented, in Tillman's view, by superpower guarantees, and, if desired by Israel, by an explicit American guarantee of Israel's security.

But as Tillman sees it, the Arabs and Israelis have demonstrated conclusively that they are unable to reach agreements without heavy pressure from the outside. He concludes that the US must attach conditions to future American military and economic assistance to Israel, which, if not accepted, would result in Washington's telling Israel: ''You are on your own.''

Tillman points to President Eisenhower, who, in 1957, compelled the Israelis to withdraw their forces from the Sinai after the Suez war. Eisenhower made it clear that, if necessary, the US would support United Nations sanctions against Israel and raised the possibility of removing the tax deductibility of donations to Israel by US citizens.

But since the time of Eisenhower, Tillman argues, the Israeli lobby has consistently preempted American Presidents. Time and again, says Tillman, American leaders, fearing political reprisal, have assured Israel that the US would never use its aid to pressure Israel to act against its preferences, even when those preferences went against American interests.

Tillman says every President since Eisenhower has ''reinforced, and apparently solidified, the conviction of Israeli leaders that it is both feasible and safe to defy the United States.'' Witness the recent Israeli bombings of Beirut, where, despite President Reagan's disapproval and warnings, the Israelis did as they pleased.