We can't confirm this one for ourselves, but we have heard "mid-July" in the past. That said, this sounds very possible. Could Mac OS X Lion be on its way for a July 14th release date? Earlier today the Gold Master was released to developers, and that's typically about as close to the final product as you get, unless there is something major that needs to be fixed. That probably won't happen though (you may remember iOS 4.2 GM 2 being released after some wifi issues with the iPad).
If the July 14th release date is in fact right, it's time to start saving. Wait a sec, it's only going to be $30 bucks, which isn't a bad deal. That's the same price as Snow Leopard, and it didn't do anything noticeably different. Lion adds quite a few new–and desired–features to Mac OS. Oh, there is going to be a server version, too. That's going to set you back $50.
Website 9to5Mac, which originally reported on the rumored release date mentions that it's possible, but adds that they "cannot confirm" that the new MacBook Air will launch alongside Lion. They do reason that it's possible. If you see all the Lion advertising, they make heavy use of the MacBook Air.