Lynch didn't play alot of the rhythms in the studio. That was most likely Don Dokken. I know dokken is a gibson freak, so it might be one of those big bodied acoustics with a sdc sent through a limiter. This is just a guess.
It's been awhile since I heard those tracks but if I remember correctly it sounded like clean electric guitar plus acoustic and an 80's level of chorus added in there for good measure.
Lynch's sound on Alone Again sounds to me to be a split humbucker on an electric (half of the bridge humbucker and the middle single coil) with a good drenching of that "80's chorus" Cloneboy mentioned and more than likely doubled by an acoustic (ala "Fight fire with Fire"). Sounds too thin to be a Les Paul so my guess would be it was an ESP. I'm also pretty sure Lynch played Randall amps at the time Tooth and Nail was recorded.
I read an interview with George when he came out with Lynch Mob, and he said the first Dokken album was recorded in England on British Marshalls, and ESP guitars. They couldn't afford to buy decent amps when they got started, so the amps were loaners, and he has been searching for that tone ever since. He's not even sure how he achieved that tone. It has something to do with the different polarity of the electric current in England is all I know.