One thing missing from your posts is where you are located. If you have access to an Apple Store Genius Bar, I would opt for taking it in. They would be in a good position to resolve your situation with the unfortunate personal circumstances you describe.
It's too bad that for your particular machine, you don't have a "physical media" option. You see, some users can buy a Lion install flash drive to perform exactly what you are wanting to do. The problem is, that the flash disk Apple sells, is not usable on 2011 Airs and Mac Mini's, as the version build predates the release of those two units. Sooner or later, Apple will undoubtably upgrade the flash drive offering, but I don't see any information as to when.
If it were legal, I would send you a copy of the full compatible installer, which I made from a legally downloaded upgrade of version 10.7.3. I have used it on my 2011 MBA, successfully. However, I think that Apple does not permit users to share in this manner. But I think that any competent Apple Store should have the same software available, that can be used in this manner. I hope this is not just idle speculation, so you need to ask (The Apple Store)
The only other option is to gain access to a good Internet connection, and reliable power source for the duration of the recovery download.