I'd like some clarification in your question. Are you asking about the last "Waterloo-style" battle or the last battle with "line infantry"? Disregarding that the latter description of "line infantry" itself is a bit problematic and would require more specification for precisely what you're talking about, those are completely different questions with completely separate answers. The former is concerned to when were the weapons of Waterloo phased out for new ones and hence new battlefield tactics developed and the latter is a question of an overall doctrine shift and major reorganization of how infantry would be deployed.

Battle of the Somme, possibly?