It will work, although it will not be legal.
It will workIt will work, because OS X doesn't care what AppleID it was bought with and you can easily buy new apps using any other AppleID. IfI.e. if you have more than one AppleID you can use any to buy apps and they don't have to match the one you bought Lion with. It will slightly complicate the apps update process, but it will work without any problems.
It will not be legalIt will not be legal, because you will be using OS X Lion bought with someone else's AppleID - not yours. So you are not legally allowed to use it.
In your initial question you ask whether you can transfer Lion purchase from one ID to another. No. Apple's policy does not allow transferring purchases between IDs.