Lyon's game-winner capped a 7-0 run down the stretch that rallied the Wildcats (8-0) from a 64-58 deficit with 2:44 remaining.
He finished with 14 points and Solomon Hill struck for 18 as Arizona pulled off an emotional victory on its home court.
Nick Johnson also reached double figures with 15 points for the victors.
The Gators (7-1), meanwhile, fell for the first time this season despite going 10-of-18 from 3-point range.
Mike Rosario scored 16 points and Erik Murphy added 15 and seven rebounds for Florida.