I think his birth year is 1760 or ‘61. 

Lestat turns Louis in 1791. At that time, Lestat’s been a vampire for 10 years, and he was turned when he was 20 or 21 (it’s UNCLEAR, there’s a debate about this)(even AR doesn’t remember). 

So Lestat is 30 or 31 in 1791, which would make his birth year 1760 or ‘61 ;D

I got a similar ask a few months back, it’s got a little more thought on the subject. There’s a timeline in the official Vampire Companion (there is some debate about discrepancies of this book to canon, but this book was intended to be the author’s deciding word on canon facts):