RE: Old Lyman
Welcome to the forum. It's nice to have you here.
Guessing by the age of the rifle it is probably a Lyman Great Plains rifle. Check the rifle and see if the barrel is not 32" and it has two wedge pins. If it is an old GPR it would have a 1-66 twist. They are roundball shooters. If it is a .50 caliber it will shoot a .490 or .495 grain patched roundball. Load about 90 grains of powder and it should shoot just fine. The older GPR's were kind of powder hogs as I remember. If it is a .54 caliber, then it will shoot a .530 or .535 grain roundball and again, with 90 grains of powder it should shoot well. Do to their length and weight the recoil with them is not bad at all.
If it is a shorter rifle, it would be their Trade Rifle with a 1:48 twist. Again the same loads apply, or you can try some Lyman Maxi ball. Although with maxi ball cut the load back to about 70 grains and work your load up.