Two problems - the .308 is a much higher pressure cartridge, which likely exceeds the design strength of the 94, and the max overall length of the .308 is about a quarter of an inch longer, meaning it would be highly unlikely any useful handload would cycle. On top of the challenges of converting from a rimmed bolt face and extractor to a recessed rimmed cartridge. And, you would still be stuck with blunt bullets, since pointy bullet noses can, and very occasionally do, cause chain fire in tube magazines.
There are good .308 lever guns in .308, which might be a much simpler way to go, although without the technical fun of solving all of the above problems!