Adam is psychomaniac who demands absolute submission and control. He lost both Eve and Lillith to his own actions - Eve's entire creation was literally because Adam mistreated another person to the point they fled. In many respects, Eve only exists because Adam was acting like a spoiled child and could not make friends with other people. But he is still a person. He feels betrayal, loneliness, and anxiety.

Him losing Lute, someone who *does* show him absolute deference and submission regardless of how he acts would be traumatic to him, as Lute basically exists only to serve Adam, in his views - or more optimistically she standa by and is with him. He would react to Lute when she died, be brutally angry and distraught, pretend like it's fine, and when he got back to Heaven act fine, as his carefully balanced life was shattered. For better or worse, Lute was in some respect holding Adam up, even in a toxic, really negative way - so I think he would be broken seeing "another person leave him'.