What ML techniques can be used to determine context across sentences?
What you want to do is to extract the relation within the sentence and in this case beyond - so basically a cross-sentence relation extraction.

Ambiguity and the context of words is a big deal when doing this kind of task. There might be multiple ways to get there, but it also depends on your goal (production environment, research or just doing it for fun to get into NLP). 

I would recommend you looking into Graph LSTMs (e.g. this Paper)