Where I can find the classification of 2transitive and 3transitive Lie groups?
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I found the following by googling : Kramer, Linus. Twotransitive Lie groups. J. Reine Angew. Math. 563 (2003), 83113. also available as arxiv:math/0106108 It completely classifies locally compact sigmacompact groups $G$ acting effectively and 2transitively 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 3transitive cases, which should not be too hard. 

