Getting a round, smooth, fat, lead guitar tone like that comes a lot from the rest of the mix, particularly to the rhythm guitars. You are never going to pull off a tone like that Orianthi chick has here in a modern metal mix with with up front, in your face, cutting, grindy rhythm guitars, it will never happen. It will get swallowed or be muddy. It takes smooth or even dull rhythm tones (if distorted) and a mix that leaves a ton of space for the lead. Distorted rhythm guitars don't exactly supplement a lead guitar tone IMO.
Besides that, obviously depends on the player, instrument, badass passive pickup, rich sounding amp, a great room sound, etc. The usuals. Goal is to capture the room sound of the guitar and let that shine in the mix without too much interference.