Thank you!
And actually, there is a way!
beware spoilers ahead
Firstly, if you outright refuse their request, they'll leave on a more hopeful note;
And, if acoite's insight is 35 or higher OR his affinity to "the abyss" 10 or higher (which can only be unlocked if acoite was a bad kitty on day 6 and is currently on godly probation) then you can actually talk to lich a little further without making them cry;