Could I write, "Li lasis lian mantelon en la domo" if it were someone else's coat he left in the house?
Sure can if you are talking about a different man.
So that answer should be accepted, as in english it isn't clear that "his" is "his own".
Yes, of course it should. Does it not accept it?
FWIW, both "lian" and "sian" worked for me.
It's not clear in English?
I would say that "John left Mark's coat in the house" is a possible, but extremely unlikely understanding of this sentence.
Why is it sian instead of lian?
Sian is his own coat and lian would be his coat as in someone elses coat. Sian could also be her own coat and ŝian some other females coat.
Yep, it's a reflexive pronoun that refers to person doing the action (verb). Li lasis sian (his own) mantelon...