You'll have to sacrifice a bit of lawn because you'll need to get as big a root ball as you can. If you take the turfs off carefully you can probably replace them with minimal damage afterwards. Wait until its dormant though. You'll need to decide whether you are going to try to make a standard - once its out of the ground have a good look at where all the smaller growths are coming from - you may find it obvious where to cut them off low enough for them not to grow back.

It might not be possible to transplant this sucker - Robinia is shallow rooting, and the roots spread out not far under the surface. The likelihood is, this sucker is coming off one of the major roots not far down below the surface, and it may have no roots of its own, being supplied by the major root coming off the main tree, which you should not cut, break or otherwise damage.