What is the value of a lever action Marlin 22 rifle with an octagon barrel Serial Number 57068 with a Bullseye on the buttstock the Marlin trademark used since 1922?

I would guess this is a Marlin model 39, but that's the only thing I can tell you for sure. Condition of collectable firearms is necessary to estimate values. If I asked the value on my classic Chevy, I'm sure you'd want to know how the paint, interior, etc. was. Without a detailed description, or good pictures, I can't tell you. It could be as little as $50, or as much as a couple thousand. These models are getting good premiums in like new condition, but are pretty common in average to well used condition. Vall