Conservative Sen. Jesse Helms (R-N.C.) has started a campaign to oust Sen. Richard G. Lugar (R-Ind.) as the top Republican on the Foreign Relations Committee and become the GOP's chief Senate spokesman on international affairs. Lugar, who vows to fight the Helms move, is a moderate who split with President Reagan on South Africa sanctions but backed him on military aid for the contra rebels in Nicaragua. The struggle surfaced with the release of letters between the two. Under Senate GOP rules, the Republicans can choose their own panel leader, but the post usually goes to the most senior member. Both men have the same committee seniority.