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. Go through the first two steps and click on 'Next' to go on to the next step in set up. Embark on installing BlueStacks App player by simply clicking on the installer once the download process is fully completed. 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. How to Install Asphalt Xtreme: Rally Racing for PC or MAC: Begin with downloading BlueStacks emulator for PC. 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 :
