I never measured the difference, but Lottie is designed for a different use case.
The main use case would be complex animations that don't require interactive behaviour. It also requires an Animation designer to design the animation in Adobe After Effects and export it via BodyMovin plugin.
Depends on the size and number of animations, but generally not really
I prefer to have them locally because it loads faster and you can also control the loading manually like in this StackoverFlow answer.