The split second after the ultimatum came out of Lucy’s mouth, she seemed to almost regret it, but she was unwilling to back down. I get her hurt and anger at Tim for ghosting her for 36 hours, and that’s something he definitely needs to apologize for. However, kicking him out was a very unproductive move if she wanted to actually sort through what was going on with him. He wasn’t going to tell her, but at the very least you would think she’d want him around so she knew where he was, rather than sending him back off into the unknown. Also, with her ‘therapy parents’ background and canonical attempts to therapize her friends, you’d think she’d recognize that Tim’s on the verge of emotional breakdown in this scene.
But to be fair to Lucy, she has no clue what’s going on other than it could get her fired if she knew about it. It could be anything, a murder even (and it almost was). As the viewers we have extra information that makes it much easier to judge Lucy for not blindly trusting him, but Lucy is completely in the dark. It’s fair for her to put her values and even her career ahead of blind acceptance of a shady mystery.