I'm not sure I agree this is even a meaningful comparison to make - they are such different players.
What clinches the issue of whether Lingard needs to move on is for me this: Where does he fit in a 4231?
He's not a winger, either by instinct or skill. He lacks the speed, dribbling and crossing ability to generate offense from out on the flank. Like Rashford and Greenwood he prefers to cut inside, but he doesn't really have quite the skill level required to do that well as a link-up player, nor the finishing ability to be a direct threat from the corners of the box. He's not a striker. And he just doesn't have the vision, patience, passing or processing to be any sort of credible No 10.
In fact, you could argue he doesn't fit snugly into any attacking role in widespread use. Maybe what suits him best is the role he used to have for England, as a central offensive midfielder drifting wide on the attack.