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The Lyman GP bullet is a flat-point, flat-base bullet with deep grease grooves. It is very different than the Hornady GP, which is a hollow-point, hollow-base bullet with shallow grease grooves. There are MANY factors which influence the way that a cast bullet actually performs. A few of them are:
1. Quality of the casting - voids, surface imperfections, poor roundness, and so forth move the actual center of mass away from the spin axis of the bullet, which results in a random transverse velocity when the bullet exits the barrel. In my experience the factory-cast H GPs are very uniform and completely free of surface defects. I suspect that most user-cast L GPs are less perfect.
2. Loading process - If it takes force to start the bullet down the barrel, the bullet is likely to be deformed, and to wind up misaligned with the barrel. That has the same effects as casting defects above, as well as accuracy issues due to powder gasses escaping more on one side of the bullet than the other as the bullet exits the barrel, and due to aerodynamic effects after the bullet clears the muzzle.
3. Bullet design and dimensions which are a good match to the barrel: A conical bullet which fits the barrel properly is MUCH easier to load straight, and without damage, and provides much better accuracy. There are two basic ways to accomplish this:
The Hornady GPs have a tapered design in which the base driving band is considerably smaller (about .495) than most .50 caliber barrels (about .501), and the driving bands increase in diameter towards the tip of the bullet. That makes it fairly easy to load the HGP straight. The Hornady GP compensates for this with a hollow base, which engages the rifling upon firing. While the Lyman GP's also have a tapered design, their flat bases are about .500 (or a little more if an alloy other than pure lead is used), which makes them harder to start straight in most rifles. Both bullets have forward driving bands which are about .508, which means that after the base is started, considerable force is needed to engrave the rifling into the bullet and push them down to the powder. However, the Hornady bullet's smaller base means that it will at least be fairly well aligned to the barrel at the point where force becomes necessary. I'm guessing that differences in ease of loading and possibly also in quality of casting may account for much of the difference in accuracy reputation between H GPs and L GPs.
Cylindrical bullet designs (all driving bands the same diameter) have to be a really excellent fit for good accuracy. Their driving bands have to be small enough that the bullet can be loaded straight and without deformation, but not so small that the bullet will not engage the rifling and stay on the powder once loaded, and not so small that upon firing, the base will allow too much powder gas to get around the bullet before the force of firing compresses the bullet and thus seals the bore. Thick felt wads often help accuracy because they help with initial sealing, and they protect the base of the bullet against the shock of firing and against gas getting around the base. Bullet-to-barrel fit tolerances for cylindrical designs are .001 or less, and because every barrel is at least somewhat different, it means custom fitting with either a custom mold, or an adjustable sizing die.
Most commercially available full-bore conicals have a tapered design because they are compatible with a wider range of barrels. The No Excuses custom bullet casting company offers its cylindrical bullets in ranges of diameters, and sells "sizer packs" to help a customer decide which diameter is right for his rifle. Unfortunately, the actual diameters of the bullets in the No Excuses sizer pack that I bought were very different than the diameters they were supposed to be. That rendered my sizer pack mostly worthless, and reflects poorly on No Excuses quality control. I suspect that bullets from the Lee .515 mold that you reference above will be quite hard to load in most .50 caliber MLs.
