For good results, a lawn needs more than 3-4 inchs of top soil. I'd
get an absolute minimum of 6, preferably 9 down. If you're going to
do this, it's easier and cheaper to do it right the first time.

As long as the water is draining through the plastic that is below the
stone base that is there now, it should be ok to put the top soil over
the stone/plastic. Check it after a heavy rain and see how quickly it
drains.

Of course, to add a decent amount of top soil, you need to have the
flexibility in the grading to do this. Make sure you grade it away
from the house. Depending on constraints, you may have to remove
material that is already there before you can put top soil down.