Is it feasible to lay new turf on an existing grass lawn?
The idea is to completely spike the existing lawn, cover the lawn in lawn dressing, then lay new turf over it.
Having turf laid is expensive, and it's worth having it done right. I would say laying turf over an existing live lawn, with less than 6" of topsoil on top, is a bad idea. It will be trying to root down while the old lawn is trying to push through. This can cause large areas of dead, dried turf.
Instead, either kill the existing lawn (cut and bag, then spray off with herbicide), and then work the top 3" of soil to lay the turf on, or get a turf cutter and remove the existing turf, work the top layer, and lay the new turf.
Make sure it is laid tightly, with no space between pieces (although you don't want overlap either). Light tamping/rolling will remove air pockets and increase root/soil contact for better rooting. Keep the area well watered until the turf has rooted strongly and is growing well. At that time you can treat it as an established lawn.