My internet connection cuts in and out every half hour or so and I can't change that,
Therein lies the problem. Downloading a 4GB file requires a steady broadband connection so the download doesn't, "time out" which is what you are experiencing. There is no resume button available if the download times out.
You could try clicking Store from the App Store menu bar then click Check for Unfinished Downloads.
And keep in mind, "reinstalling OS X Lion via Lion Recovery requires broadband access to the Internet via Wi-Fi or an Ethernet connection. OS X Lion is downloaded over the Internet from Apple when Lion Recovery is used for reinstallation". From here > About Lion Recovery.