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Lucas offers his cabin to Carla Ruiz to not only get away but to protect her possibly from maddog. He then begins a sexual relationship with her. Was this unethical given she’s a victim and a witness in his investigation?

Yes it is but it sounds like it is Lucas' MO. His commander knows it, his girlfriends know it, and so does his fellow detectives. He gets woman to sleep with him and Lucas doesn't even try,

Yes, completely unethical until the case had been completely resolved [I would think].

I am not sure quite what his attraction was, although I'm sure his vehicle (thanks to his gaming inventions) and his brains were part of it.

Yes, it was unethical.