Maybe someone else has another idea about this, but the portal to the Mac App Store is on Snow Leopard, 10.6.8. So you will first need to install Snow, then run the Combo update to get to 10.6.8, then, for Lion, it is my understanding that you will have to call Apple and purchase the code for Lion (it's no longer on the MAS). OS upgrades are tied to Apple ID's and if you didn't purchase Lion originally, you won't be able to simply re-download it from the recovery partition.
Although it's no longer being supported by Apple, you may want to stick with Snow, at least for the time being. Lion has a number of issues that were corrected in subsequent OS versions, and you may not be happy with it. But I wouldn't use the native Safari browser, which hasn't been updated in quite a while. I'd get either Firefox or Chrome, which will be far safer.