I’m totally unqualified to answer your question, but since it’s been a few days, I think maybe this thread might be related to your question:
Cardio: Is it better to split the long runs, or do them in a few big sessions
It’s in the powerlifting vs endurance training context and doesn’t answer your question about whether to run first or lift first, but it does talk about the compromises involved. For what it’s worth, I’ve always read that you want to lift while recovered as much as possible, so I guess if someone told me I’d have to do both in a day, I’d lift first.