I tried to install the latest version of Android studio on my OS x 10.7.5 but the AVD requires 10.8.5 or higher upto 10.9. It is not possible right now to update OSx, instead we decided to get a working version of android studio.
Which version of Android studio would work on Mac OSX 10.7.5?
There are three options from what I see here :
You install ubuntu (I recommend Linux Mint 17.2 "Rafaela" - Xfce RC (32-bit) as it's lighter on your CPU and RAM) and dual boot. You don't need to update your Mac OS 10.7.5, it will remain intact, but you will boot on linux to develop Android Apps.
There you can install the latest version of Android Studio with no hassle.
Go with the previous Android Development solution : Eclipse IDE Indigo or higher + ADT bundle plugin. Check to see what version of JDK worked on 10.7.5, install it, then install one of the versions of eclipse from Indigo to Mars and then install the above mentioned plugin.
You can try to download and run the first Android Develop Studio Beta that ever appeared on the website (0.8.0), I don't think they ever supported 10.7.5, but you can try.
My suggestion is to try to install linux (point 1) (maybe with the help of a friend), because it's important to have the latest SDK version and the latest updates.
+ It's easier to work with.