Catch 22. Apple is the software manufacturer, so you may need to contact them for this specific issue.
AirPort Utility 5.6 will not install on Mountain Lion 10.8.x either, using Apple's installer. But, there are several workarounds that seem to allow this.
One of them is discussed in this article:
http://www.macworld.com/article/1167965/mountain_lion_and_the_ancient_airport_ba se_station.html
I do not have a Lion 10.7.5 Mac here to test, but can say that the workaround does work on Mountain Lion for me. Follow the instructions in Pacifist to manually "extract" the AirPort Utility 5.6 application and install it in the Utilities folder on your Mac.
It might work on Lion, if you want to give it a try. Otherwise, if you do not want to contact Apple, you could use another Mac....if available.... running an earlier operating system to configure the Express. Even a PC would work for the same purpose.