New lawn

Can I lay new turf over an old lawn?

 

As long as you prepare the soil properly first.:gnthb:

 

As daitheplant mentioned its really important to get a decent tilth going to allow for good root penetration once the lawn has settled a bit and started to push its roots through. Otherwise you will have the existing lawn warring with the new lawn, and once the lawn underneath starts to rot that can interfere with the new growth.