Don't worry about the series 7... very few firms still require it. Only if they are registered as broker-dealers is it necessary. Look into the Schonfeld owned firms... I would assume most use or have access to Lightspeed considering he owns it. I traded for a prop firm that used Lightspeed, but its no longer around unfortunately. T3 I think uses it too.
If you are looking for a prop firm that uses lightspeed, I know that WTS now has a Lightspeed option and you do NOT need your series 7
WTS is thinking of switching to Lightspeed from Sterling. They already let some people try it when I was there. You don't need any license to work there.