I shoot only patched ball in my .50-caliber Hawken-pattern rifle, so I never have a leading problem.
However, in my cap and ball revolvers I've found that pure, soft lead is best. It never leaves metal fouling in the bore.
Years ago, I cast some balls for my .36 Navy of wheelweight metal because it was all I had at the time. This alloy left leading in my bore. Very soft, pure lead does not. Go figure.
In both my rifle and cap and ball revolvers, I use a lubricated, hard felt wad over the powder and under the ball (patched in the rifle, nekkid in the pistol).
I lubricate the wad with a very old bullet lubricant recipe that undoubtedly dates to the 19th century:
1 part paraffin (I use canning paraffin, found in a 1 lb. block in the grocery store)
1 part tallow or lard (I use mutton tallow, sold by Dixie Gun Works. It seems to make the slickest feeling lube)
1/2 part beeswax
All amounts are by weight. I use a kitchen scale to measure 200/200/100 grams of ingredients, then put them in a quart Mason jar. Add the filled jar to a kettle with 3 or 4 inches of boiling water, for a double-boiler effect (the safest way to melt greases and waxes).
When all ingredients are melted, stir well with a clean stick or a disposable chopstick. Remove from heat and allow to cool at room temperature. Hastening cooling by plunging in ice water or placing in the refrigerator may cause the ingredients to separate.
Screw a lid down tight on the Mason jar and store in a cool, dry place. I store mine in a spare room, alongside the raw mutton tallow, and have never had it go rancid.
To lubricate felt wads, such as Wonder Wads sold by Ox-Yoke, place about 2 Tablespoons of lubricant in a clean tuna or pet food can. Place on the burner at very low heat, just enough to melt the lube. Now, add 100 wads or so (perhaps 50 for wads larger than .50 caliber). Stir the wads in the lubricant until all wads are well-soaked with lubricant. Add more lubricant if needed.
Allow the can and its contents to cool at room temperature. When cool, snap a plastic pet-food top over the can and you now have a container to take to the range. When you run low on wads, simply add more wads and lubricant and return to a low heat to replenish your stock.
The can does double-duty as a melter and container.
To load your rifle, add a measured amount of powder. Then gently ram the greased felt down gently, taking care to not tip it in the bore. Seat firmly against the powder. Follow this with a patched ball or, in your case, the Lee REAL bullet.
A felt wad doesn't work well with bullets that are hollowbased, such as those found in the .58 Civil War rifles. The wad interferes with the swelling of the rifle's skirt by hot gases and affects accuracy. But the REAL bullet has a flat base and shouldn't be affected.
You'll find that this extra step of seating a greased felt wad will keep your bore remarkably clean.
You'll also find that you needn't seat the wad each time you seat a bullet. If I'm in more of a shooting than loading mood, I'll load a greased felt wad every other time.
In my .50 rifle, with its basic sights (and my 49-year-old eyes) I can't tell a difference in point of impact at the ranges I shoot (25 to 100 yards). However, your own experience --- especially with that Lee bullet --- may be different.
Experiment. That's part of the fun of muzzleloading.