Right. That Auster is influenced by psychoanalysis seems quite clear. That is himself has been in therapy is possible as well. That he has read Lacan AS WELL AS FREUD seems extremely likely. But
a) I dont think his work, in the state it is, whether it's intentional or not. is influenced more by Lacan than freud. (lacan having been more than influenced by freud this would explain that)
b) Lacan, nor Freud are philosophers whatsoever (despite the widespread vulgarisation). The purpose of their writing or psychoanalysis, is completely different. And while one will find overlaps in all and any disciplines, that's it.
c) Fiction, Auster's territory, has even less got anything to do with philosophy and the purpose of fiction has got nothing to do with philosophy either. That it necessarily invites you to self reflect, does not mean Auster needs you to share his views or wants to spread any truths, nor wants to cure you. It's about sharing emotions and style.
Now back to your point, yes I think it's very likely that Lacan and therefore Freud have influenced Auster. And in many ways, while it's certainly more pronounced in his work, well, which modern writer hasn't. (be it unconsciously)? :)