The request to the office of Sen. Richard G. Lugar (R-Ind.), new chairman of the Senate Foreign Relations Committee, was routine: Would the senator please reserve a congressional hearing room for a briefing next Monday by the Fusion Energy Foundation on the economic benefits of President Reagan's Strategic Defense Initiative, or "Star Wars" plan?

Lugar's office, which gets dozens of similar requests, did what it normally does for worthy-sounding causes: swiftly reserved a room in the Dirksen Senate Office Building.

Yesterday, embarrassed Lugar aides just as quickly canceled the reservation when informed that the foundation is an arm of the controversial organization run by Lyndon H. LaRouche Jr., a right-wing presidential candidate.

"It was an innocent but stupid mistake," Lugar aide Mark Helmke said. He said he informed foundation officials yesterday that the room had been canceled, telling them, "It's nice that you support the president's proposal but the chairman doesn't want anything to do with your organization."

The Fusion Energy Foundation is one of the more visible arms of LaRouche's organization. It seeks to promote nuclear power and "beam" weapons. A one-page announcement of the foundation's briefing, which was received by members of Congress this week, heralded the "technological revolution" that it said will spring from the president's space initiative.

According to Helmke, Lugar frequently is asked by groups, most of them based in Indiana, to reserve a room in one of the Senate office buildings for a news conference or briefing. Any member of Congress can request that an outside group be allowed to use a hearing room.

In this case, he said, a new secretary processed the request without clearing it at higher levels, as is usually done; thus no one spotted the group as one with which Lugar might not want to be identified.