I take it then there is no time limit on the Committee hearing it just will simply run out of time.
The committee (Foreign Relations) is a standing committee which holds hearings on anything to do with foreign relations - ambassadors, treaties, legislation, etc.. The Chairman is always from the majority party and the majority party has more members on the committee, depending on the ratio in the Senate. Right now there are 10 Republicans and 8 DemocRATs on the committee.
The chairman calls the meetings and sets the agenda. So Lugar can just wait them out.