You do need the lubricant to help the patch seal the ball. Powder should be real black powder and Goex is fine. Did the previous owner provide any suggested loading? I don't think you told us the twist rate. At this time it doesn't really matter as you will be changing powder loads to develop your most accurate load.
So what I have as a starting load to begin developing a load is 0.480" balls, 0.025" thick cotton patching, damp lubricant with a Ballistol(1)/water(7) parts mix, and 70 grains of 3fg GOEX. Use your measure to increase the load by 5 grains. Use a damp thin cleaning patch (loose jag) between shots to have a consistent fouling level in your barrel. Your jag may be need work as a 50 cal jag will only push fouling into your breech. Its time to quite overthinking this and get out there and start shooting. You will need a notebook or camera to record the effects of changes in load. Hmm, sounds a lot like Flehto's load.
Yes, I am using Dutch's dry lube formula and my patching material compresses to .018. The jag that was included with the rifle seems pretty good with an oiled flannel patch around it plus I have 2 other jags in "50" caliber that I will try to see which has the best fit. I only use Goex now but there was a time that I had to try all the substitutes and plastic skirted pistol bullets; lessons learned the hard way. I'm tempted to call this a 48 caliber as I've never heard of a 49 but given that it was common practice to have a rifle barrel re-bored or "freshened" after accuracy dropped off I can imagine that a Hawken might start life as a .48 and then, if it survived a few decades, end up as a .54 or somewhere in between. I haven't measured the twist rate yet and the seller didn't include that information. I actually traded this Hawken for a 50 caliber, LH TVM Early Virginia flinter to the same friend who sold it to me a few years back. The TVM didn't quite have enough LOP for me so that same friend traded a Dutch Club Butt fowler for the Hawken, then traded that to me for the TVM that he sold me years ago. The Hawken is left handed and has a 15 inch LOP to it fits me perfectly but it's a 10 pound plus rifle; a real monster compared to my other muzzle loaders.
At any rate, the seller of the Hawken had never shot the rifle and it was custom made for someone else. I don't know exactly how he came to have it but I will figure out the twist rate here soon. Thank ya'll for all your help as this is a new one on me.