You can use compost but you are better to use a dressing made out of peat, sand and a fine compost. I rake in this after scaryfying the lawn and adding some seed. It is still early to do these things - April is normally the ideal time.
Don't use compost if your drainage is poor, I used a compost/sharp sand mix after scarifying and aerating last year and made it worse.
Meant to do it again with just sharp sand but as a result of last years shenanigans haven't been able to walk on it!