That's one of those simple questions with a complex answer. It's akin to saying, I'm having a 458 lott built, how accurate will it be. The answer to both questions is, it depends.
What are the dimensions of your barrel and throat, how smooth is the bore, what is the barrel twist, what lead alloy are you using, how hard is the lead, what lube are you using, what dia are the bullets sized to, what powder are you using and what peak pressure is your load generating.
All of those factors affect what velocity you can reach in a rifle with a cast bullet, retain accuracy and prevent leading.
You certainly can run a 300 gr cast slug to 2700+ fps from a 458 lott, but whether or not you can do so accurately is not a simply yes no answer. 2200 fps seems to be a threshold at which one can achieve accuracy with no fear of leading with little effort in the average rifle. Some rifles can get up to 2400 fps without much muss and fuss.
Personally I'd look at a 400 gr cast bullet @ 2200 fps as a goal. That combo should be capable of good accuracy without a doctorate level cast bullet approach, and it'll be shootable. I've shot the 458 lott enough to know when increasing bullet weight and velocity, the joy of shooting the gun quickly diminshes. But if you just need more from the lott, look at increasing bullet weight, not velocity. I've shot 500gr cast @ 2200 fps, reasonable accuracy and gives you the full lott experience. You might even try 550 gr cast