Slugging the barrel is the only way to be sure.
That said, since your rifle is recent production I'd assume it's made by Miroku. My 1885 High Wall 38-55 is also made by Miroku and the barrel slugs an exact .375" groove diameter. Since the barrels are made by the same Japanese company (folks not known for their sloppy machine work) and likely bored and chambered using the exact same tooling one could deduce that yours is also .375. Not conclusive but a good place to start.
AFAIK all .375 jacketed bullets are going to be .375" so there is no choice there. I used cast bullets sized to .377" to get the best groups in my barrel.
Of course, with cast bullets you want to match the throat diameter, not necessarily the groove diameter - that's why I went with .377", but that's a whole 'nother topic by itself. You could ask about this on the cast bullet forum but be prepared to be led down multiple rabbit holes.
One other caveat or perhaps bit of advice. When I first started looking at reloading the .38-55 it seemed that die sets varied almost as widely as bore dimensions, especially the neck expanders. Unless something's changed in the last few years, calling or emailing the various companies gets no useful info since their customer service folks either don't know or won't tell you the diameter they use. RCBS makes a Cowboy die set with two different expanders, one is .379" and the other is .376". The smaller diameter worked well with the .377" cast bullets and even with the .375" jacketed bullets. Having a single shot I never crimped case mouths but you'll want to do that for your lever rifle.