This is a very good question, because the ability to link your purchase to your iTunes account it tied in within the actual purchase from the Mac App Store. I have read, but cannot confirm, that when you purchase a new Mac that has the drive included, they will "credit" this against your iTunes account (or provide a facility to allow you to do this).
New Macs with the stick included are in an odd situation, because they come with the drive, but also come with the Recovery partition included as Firmware (not as a disk partition) that will allow you to re-install online. The online install option required authentication to prove validity, so this would be useless if they did not make the connection somehow. I think actually it's related to your system serial number, they know it was sold with Lion, so they will let you download even without a purchase history or Apple ID connection.
It should be noted that the Ts&Cs for the stick suggest that once you have installed via the retail thumb drive, you cannot then subsequently reinstall or recover using the recovery partition, in fact I believe that it does not create one. Some suggest this is because there is no mechanism to link the thumb drive purchase to your Apple ID.
I think the best solution is to avoid the retail stick, purchase Lion through the MAS, and then burn your own install DVD/USB/HDD installer from the package that you download. This get's it linked to your iTunes account and provides the license to do multiple installs, and provides you with both the means to do a full local restore without internet connectivity, as well as online recovery.
Whether this is technically against the license to install on your partners machine is hard so say, depends, I suppose you could own the machine, but just not use it as the primary user - there is no problem with his/her machine being subsequently used by a different iTunes ID. The spirit if the MAS license is all your home PCs, which I take to mean all the ones in your home, not just the ones which legally belong to you. Unlike purchases from the MAS the OS does not require you to have proof of purchase to install etc.
EDIT: Put it this way in summary, the multiple install license is a feature of the Mac App Store, and not specific to Lion. Purchasing Lion outside of the MAS might not afford you the same rights, certainly it removes the right to do online restores.