If they get the West Ham version, he could honestly keep them up or outside the relegation dogfight, and if he manages that, he'll have been worth every penny. Don't forget, they're essentially paying him with their PL bonus promotion money. He's a scrutinised investment to that end, which makes sense from their side just as much his and they're covering their bases should they be relegated.
I think people forget that Lingard has more to gain by going there and performing superbly than coasting. He's not just playing for the most he's worth on an open market now; he's playing for his future, and what will be the biggest contract of his career if he delivers for Forest.
If he repeats that West Ham form in an inferior team, his stock will go through the roof because he'll be a certified and bona fide PL performer who has proven he can both carry a team and prove he is worth every penny of a longer term contract.
He should be setting his sights on the likes of Newcastle and that jackpot money. They've not gone bonkers in the market yet and he, at West Ham level, would be very useful for them indeed for a while. Initially a starter, but with a long-term eye on him supplanting him and having come off the bench. If Lingard has the contract he wants, I doubt he'll care enough to kick up a stink by then. He'd be 31 or so by then, also.
This could be one of the smartest moves of the summer for both player and club - a mutually beneficial partnership where they're using each other to achieve an objective. Of course, your perception of such will come down to how good/bad you think Lingard is as a player, and whether you think he can repeat his West Ham exploits with an inferior team, or at all, for that matter.