I have a couple of Tikka Varmint rifles. One is a .223 & the other a .308. While these are probably a little heavier than the Tikka Lite, I'm sure a person could do some mods to add some weight. I did put a brake on the .223 & can hardly feel any re-coil at all. The .308 could use one, but I shoot F-TR with it & can't use a brake. I also used some sticky lead wheel weights inside the stock. Not really to add weight, it's there for better balance. I don't know why you couldn't just add more of those to help reduce re-coil in the lite.
If you're riding' ahead of the herd, take a look back every now and then to make sure it's still there.