You can hear his mother's pronunciation of the name in this interview of her experience of the months and years before -- and after -- his birth (audio link on top).
One of the first times I saw Lizzy live, I asked a swag salesman outside the venue (a brit) how it was pronounced. He looked gobsmacked for a second, then he said "Lynn-it".
Then during the show, when Phil was introducing the band - "Brian Downey on drums" etc - he ended with "Phil Lie-nuht on alcohol".