I think that this has something to do with what's called A-homotopy theory. In fact, the following two papers on A-homotopy theory reference Lovasz's paper, and from looking at the first paper below it seems like it's exactly the sort of thing you're looking for.
MR1808443 (2001k:57029) Barcelo, Hélène; Kramer, Xenia; Laubenbacher, Reinhard; Weaver, Christopher Foundations of a connectivity theory for simplicial complexes. Adv. in Appl. Math. 26 (2001), no. 2, 97–128. (Reviewer: Andrew Vince), 57Q05 (05B35 05C10 55P99 55Q05)
MR2163440 (2006f:52017) Barcelo, Hélène; Laubenbacher, Reinhard Perspectives on $A$-homotopy theory and its applications. Discrete Math. 298 (2005), no. 1-3, 39–61. (Reviewer: Jean-Louis Cathelineau), 52B40 (05B35 05E25 37F20 52C35 55R80 57Q05)