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. Go with the previous Android Development solution : Eclipse IDE Indigo or higher + ADT bundle plugin.
There you can install the latest version of Android Studio with no hassle.
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. 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. There are three options from what I see here : Which version of Android studio would work on Mac OSX 10.7.5? It is not possible right now to update OSx, instead we decided to get a working version of android studio. Version of Android studio for Mac OSX 10.7.5 - android 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.
