Let L be a lattice in a simple, connected, real, higher rank Lie group G with finite center. We classify all locally compact groups H in which L can be embedded as a lattice. For cocompact embeddings we give a similar classification for irreducible lattices in all semisimple Lie groups, with the only exception of non-uniform lattices in SL(2, R), i.e. virtually free groups. The latter are discussed by Lee Mosher, Micha Sageev and Kevin Whyte in their recent work.