It might look awesome, but its impractical and unfeasible. In addition to the problems of temperament, there are biomechanical considerations. Check out this animation of a horse galloping compared to this one of a lion running. The horse's back remains relatively level, which allows it to support a rider. Conversely, the lion's back flexes considerably as its runs. That flexibility is great for bursts of speed and maneuverability, but it means that a lion (and most carnivorous mammals for that matter, which have similar skeletal features in this regard) can't support a rider of any significant size--dog-riding monkeys notwithstanding.

Since the main problems with using lions and similar animals as mounts are biological, you probably want to check in with /r/AskScience for a more thorough answer on that front.

i agree, and would simply like to add cheetahs to the question as well