Patchy parts on the lawn tend to be where the lawn mower cuts deep into the grass roots and soil. The only thing to do is to level the lawn. Reduce the mound by cutting the lawn and digging out some soil other is easier than adding soil and reseeding it to get a level.

Yes I agree lifting the turf and replacing it after removing some soil can work well for smallish bumps if the turf is still grassy! and dont forget to keep it watered till it takes again. You may have to do this and reseed these areas as well though?