I'd better start by saying I've not actually seen one of these lavvu's in the flesh, but I've been thinking about simple ways to extend them, as some people have said they're a bit small.
I reckon instead of trying to add fabric to the bottom the easiiest way would be to add a simple rectangle of tarp in the middle. I've seen, but can't find it a picture of of half a lavvu set up, so they'll obviously stand up like that.
The tarp would need buttons/holes to attach it, but that shouldn't be too hard to do. You'd button in one side completely and use the other side as a door. You could use a couple more poles or paddles or paracord to trees/landies/bystanders to support the loose flap and which would give a useful covered porch which could be open to your fire.
Here's a very rough MSPaint sketch which probably explains it all better.