While Brown was a student at Florida, he was initiated as a member of Phi Beta SigmaFraternity (Zeta Kappa Chapter). He later returned to the university during the NFL off-season to complete his bachelor's degree in health and human performance in 1996.
Brown is probably remembered most from his years in Detroit, where he gained the reputation as one of the league's premier offensive tackles. He was a pivotal piece on the offensive line that blocked for perhaps the greatest running back of all-time (Barry Sanders). Brown was one of the most durable offensive linemen in the Detroit Lions' history, starting all but one of the 164 games that he played for the Lions.
Along with Kevin Glover, Brown was a key blocker on a line that paved the way for Sanders, who claimed NFL rushing titles in 1990 and 1994. He blocked for Sanders for seven seasons (1989–1995), and Sanders accumulated 10,172 yards (an average of 4.9 yards per carry) and seventy-three rushing touchdowns during that time.
Brown was a member of Lions teams that made the playoffs in 1991, 1993, 1994 and 1995, and he was a member of the 1991 and 1993 squads that won the NFC Central division title. In 1991, the Lions set a franchise high with twelve regular season wins and earned a berth in the 1992 NFC Championship Game. Brown was also a charismatic and respected leader on the team, who graciously donated a great deal of time, energy and money to many charitable causes throughout the Metro Detroit area.
On December 22, 2012, Brown admitted during an interview on the SVP and Russillo show on ESPN Radio that he purposefully failed to block Green Bay Packers defensive end Sean Jones during a 1994 game so teammate and quarterback Scott Mitchell would get injured and be forced to leave the game. Mitchell's finger was broken on the play and he left the game. Mitchell was taken aback by Brown's comments, remarking, "I had Lomas in my home. . . . I'm dumbfounded that he would do such a thing. . . . [F]or him to allow someone to take a shot at a teammate, that's crazy."
Less than a week after the interview, Brown expressed remorse during an episode of ESPN First Take, saying "It's one play out of the 18,000 that I regret." He did not deny his original comments: "I'm not going to retract, I'm not going to sit here and make excuses . . . The one thing I can say is I should have been more tactful at how I said that. That was wrong on my part. I should have humbly said that. It came off boastful, and I shouldn't have said it that way. I said it, I can't take it back, but I shouldn't have said it the way I said it."