Unless the shade problem is taken care of no amount top soil, seed, or sod will give this customer the lawn he seeks.
If the ground is not lumpy, no low spots, no weeds growing through the top soil why waste time effort and money by roto tilling, laying fresh sod?
This ground should be smooth being top soil was raked over it.
Walk the property pointing out which trees need to be removed, thinned, and lower branches removed.
Then do a soil test for NPK and PH. Correct as needed.
Get a slit seeder.
Then point out he can not let the lawn get smoothered by leaves in the fall or all of this work will go to waste.