Goalkeeper Aaron Chapman, defenders Matty Brown and Ritchie Humphreys and winger Jamie Devitt have all signed contracts at the Proact Stadium during the close season having been invited to train with the League Two club.
Midfielders David Morgan and Hamza Bencherif are two more players currently trying to earn deals with Paul Cook's side.
Both have featured in recent pre-season friendly matches and Lynch has paid tribute to their hard work.
"David Morgan and Hamza both have good attitudes," said Lynch. "We know Hamza can play but we're being honest with him, and he's an honest lad himself, but he needs to be a little bit more fitter.
"He had a hard training session on Tuesday morning and with how hard he worked he actually lost 2lbs in weight. So it was testament to him that he played on (against Wolves) Tuesday night and put in a performance.
"But that's typical of the attitude and the effort the players are putting in and it's typical of the players we've looked at all summer.
"David works hard too and you can see he's a very good player. You don't be at Forest if you're not a good player.
"But it's about how he fits in with us and like we have with other trialists, we'll look at him. He's done himself no harm and it's a tough decision that the gaffer has got to make but there's no decisions being made as yet."
Morgan, 19, has been told by Forest that he is free to find a new club while 25-year-old Bencherif is a free agent after leaving Notts County this summer.