Apple says you must have an internet connection to reinstall Lion. Well, to be precise, they say:
In order to reinstall OS X Lion, you will need to be connected to an Ethernet or Wi-Fi network. The Wi-Fi menu item is in the upper-right corner of the screen. Click the icon to display all available Wi-Fi networks. Click your preferred network name and, if needed, enter a username and/or password.
but presumable that ethernet or wi-fi network would have to be one that leads to the internet.
I don't know how serious they are about that, but I do know that when I reinstalled from a saved copy of "Install Mac OS X Lion.app", which should be at least as self-contained as the Recovery HD, it still told me it was "downloading additional components". I obviously couldn't snapshot the message at that time, so I'm not sure of the exact wording, but it made me wonder if the installer would always auto-update to the latest version of Lion every time.
When I did this, 10.7.1 wasn't out yet, so the "additional components" were still part of 10.7.0, and that's what was installed. I suppose the test would be to wipe a spare disk and try again, and see whether it installs 10.7.0 or 10.7.1. A complete test would test both "Install Mac OS X Lion.app" and Recovery HD, which might do different things.
