Mike Lyle wrote:
Agreed. Unless it's very long, I don't think I'd cut it before
top-dressing, though: I think it will recover quicker if it's got its
leaves in the light.

--
Mike.

I mentioned mowing it but the thinking there was that the soil on top
would completely cover the old grass and the OP would sow new seeds.
Otherwise, I'd gradually add something over a period of time and try to
give the grass some time to grow through.