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It wasn't a game show, persay, but are you perhaps thinking of Animal Jam from the Jim Henson Company?
Between the Lions did a lot of different skits and I think some of them may have been game shows. And I know they sometimes played the fact that the main characters were lions for humor. Any chance it could have been something on there?

I know it was airing in the late 90s, maybe early 2000s but forger what channel. Maybe Animal Planet? Probably one of the non-cable stations if not. Pretty sure it involved some sort of game show with puppet animal hosts or something? I remember an episode where one of the hosts was getting antsy about a lot of the contestants or something being carnivorous and seeing him as a meal or something though that just may have been a gag.