I am a professor who runs a research lab at a university. I have a grad student who works with me, and who also has a history of lying. Most recently, he took information home with him that should have been kept in the lab (which was a breach of our IRB/research ethics). I believe that it was an honest mistake, but the problem was how he dealt with it. He told three different stories about what happened with this information, each of which contradicted the others. So, he either has a poor memory for how he handles important study information or he is flat-out lying to me (I believe the latter). I need to trust that my students follow lab procedures when I am not around and that they will be accountable for their actions. I am liable for my students' actions and mistakes.
Would it be reasonable to "terminate" the student based on this and similar incidents? (Each incident individually is below the threshold for "actionable offense," but they are starting to add up). By "terminate," I mean at a minimum that I withdraw as his advisor, though honestly I believe that it is time for him to leave the university altogether.