I've seen 100 and 1000 lot max size on retail accounts but if you honestly need more than that then I would suggest contacting your broker and moving to a professional account if eligible. You will no doubt get a higher limit but will forfeit protections such as negative balance prevention.
I believe that you don't really needs to search for a broker with the highest lot size. It means nothing actually, I think that traders have to pa yattention to other details when they're choosing a broker, because there are lots of other things which are considered to be more relevant for traders. No doubts, that all traders try to find a broker according to their own needs, however the lot size doesn't matter at all. Of course, you can have your view on this matter, I just explain my own point of view, but I never pay attention to such details when I choose a broker.
I believe trading conditions matter more than the lot size. If a broker is having tight spreads and low commissions, then you can definitely good ahead. Fxview, tickmill and pepper are a few good ones in this regard.