I'm going to -guess- that if you want to install 10.7, you may have to search for a copy of it from a source "other than" Apple.
Such "alternative channels" ARE available, although I can't really mention them here.
Others will respond to my post with the warning that such channels are dangerous and unreliable. There may be an element of truth in that, but in my own experience I've had no more trouble with Apple System software obtained from "unofficial channels" than I have with software from Apple's own sites.
Ultimately, if you want 10.7 on there and Apple won't provide it to you any longer, you "have to do what you have to do".
Editorial rant:
Back in the days of "the Classic Mac OS", one could go to Apple's servers or other large (usually university-administered) servers and freely download all past iterations of the Mac OS and relevant Apple software. Some of those old servers may still be up and running today, but are no longer updated.
Apple now makes it somewhat difficult -- and in some cases impossible -- to obtain older versions of their software when you need it.
For this reason, I have no reservations about sourcing old System software from wherever it may be available.
End of rant.
My opinion only.
Others will disagree.
Some will disagree vehemently.