Hey Billy

This is an interesting idea. I've not read much on this, nor have I come across much info on it.

with a quick google search I found a youtube video of someone growing wheatgrass aquaponicly, looking at it, it does seem like you could get the density you need to be able to call it a lawn.

Also I have seen articles on growbeds that use hydroton and soil, this might be the best way to go about growing grass.

However things you might what to consider or look into, is if you can grow a type of grass you want, and then if you did it, would it be stable enough to walk/play on, could walking on it cause compaction, if it does cause compaction, is this ok, will compaction reduce or block the flow in or out of the "grow bed" and if you are walking on this, will the grass survive.

please note that I'm not an expert, so I'm only applying the logic I have from what i do know.