Where I can find the classification of 2-transitive and 3-transitive Lie groups?
I found the following by googling :
Kramer, Linus. Two-transitive Lie groups. J. Reine Angew. Math. 563 (2003), 83-113.
also available as arxiv:math/0106108
It completely classifies locally compact sigma-compact groups $G$ acting effectively and 2-transitively on a non totally disconnected space $X$ (hausdorff I presume) : then $G$ is a Lie group, $X$ is a connected manifold, and the examples are listed sperately, according to wether $X$ is compact or not.
It remains to extract the 3-transitive cases, which should not be too hard.