It would all depend on where the panel is being installed as to the Main Lug panel.
The size of the breaker used as a disconnect in the panel (main) wouldn’t matter.
I can install a 200 amp main panel and feed it with a 60 amp feeder as long as the conductors are #6 and the breaker protecting the feeders is 60 amp. The 200 in the panel is nothing more than a disconnect and its size has no meaning at all.
If you are installing #8 feeder conductors protect them with a 50 amp breaker and the size of the breaker in the subpanel does not matter.
The Equipment Grounding Conductor installed with the feeders will need to be at least a #10 and kept separate from the grounded (neutral) in the subpanel.