Stephen Danielian scored the lone goal for the Cougars, tying the contest in the first half.
Don Browning had both goals for Bremen, now 12-0-2 on the season. Chris Gingerich had two assists for the Lions.
Bremen outshot LCA 26-7 and had a 5-2 advantage in corner kicks.
LCA keeper Logan Pitts came up with 21 saves in the game. Austin Adams had four for the Lions.
LCA is now 1-7 on the season.