Depending on the speeds at which they can travel and the size of the cage, the lion will either catch the tamer in a finite amount of time, or he will asymptoti

Depending on the speeds at which they can travel and the size of the cage, the lion will either catch the tamer in a finite amount of time, or he will asymptotically approach the tamer. Given that they're point masses, I can't see how speed and size of the cage could affect the solution. Unless the initial distance between lion and tamer also factors in.