Iyor I made a 14.5" MBE and the stone diameter I use is 12". Seems to work fine but I don't have experience with the 22.5" LBE. 20" should be sufficient. I'm wondering how big your pies will be. If the stone is 20", the max size pie you will want to make is 19" as landing a round 20" pie on a 20" stone is nearly impossible unless you build the pie on a pan. So whatever size pie you want, allow 1-2" extra for the stone and then 2" extra for sufficient airflow.
If my goal was to make 16-18" pies, then I may try a stone size of 19 or 20". Which one is better and does 1" make a difference when it comes to airflow I do not know. Hopefully one of the LBE guys can chime in.
Goodluck and we would love to see pics of the set up and the pies.