It depends on the quality of lawn you are hoping to achieve.
The secret to a good lawn is the amount of preparation you are prepared to do before you lay the new turf or seed it. And I would remove the turf and stack it separately if I were aiming for a fine lawn as bumps and hollows will be inevitable if you include the old turves as the soil will settle over time as they rot down.
My approach would be to hire a turf cutter and lift all the old grass as the first step - stacking it neatly somewhere to rot down and form useful compost. Then I would lay a 50mm layer of coarse sharp sand and rotavate that into the soil to ensure good drainage - on heavy clay a series of land-drains might be needed first.
Then set out your new level using stout tanalised boards around the area and ensuring they are firmly fixed. Top up to this with sandy, clean topsoil and compact evenly by treading it down and raking it over.
Turf or seed onto this firm level surface and you will have a fine level lawn that will be the envy of the neighbourhood. But it is a time-consuming task and it will be costly to achieve. Good luck!