Remigius Lupeikis competed for the Soviet Union prior to the break-up of that country and in 1986 won a gold medal in the team pursuit at the World Junior Championships. Later racing for Lithuania, he had a long career in the professional peloton, riding through 2002, including appearances at the 1996 and 2000 Olympics. As a professional he was never chosen to ride the Tour de France, but did race the Vuelta a España in 1992 and 1997, and the Giro d’Italia in 1992. His biggest professional victories came in winning the 1994 Tour of Berlin and the 2000 Tour of Egypt. He was also Lithuanian champion in the individual time trial in 2000 and in the road race in 2002, placing second in the Lithuanian Championship in the road race in 2000 and the time trial in 2002. On the track, Lupeikis won a silver medal at the 1995 World Championships in the point race.
Lithuania