I was trying to find the answer to this as well. I have a Mac Mini (MM) running Lion setup with an external drive that is used for Time Machine (TM) backups for the MM and my MacBook Pro (MBP) which is also running Lion. Previously, in Snow Leopard the MBP was able to select the MM's external drive as the TM backup location. After doing clean installs of Lion on both machines the MBP could never select the MM's external drive as it's TM backup location even though the MM's external drive was connected and usable in Finder. It just never showed up in the list of available drives when pressing "Select Disk" when truing to setup TM for the MBP.
I tried various suggestions on the net to no avail (the pondini TM FAQs, and some others). Nothing worked and all posts I found was of course you can use another Mac's external drive as a shared drive for TM backups. I found a MacLife.com article for "How to Connect to External Macs via AFP in Lion" that shows how to connect to another Mac via AFP by using Finder's connect to server option. After connecting to the MM as a server I was then able to choose any of the MM's volumes and mount them on the MBP (note I had to disconnect the previous Finder mounted MM volumes first). I mounted the MM's external drive and then it was an option in the TM when pressing "Select Disk". I don't know why it previously just worked in Snow Leopard, but its probably due to the changes in Lion's AFP handling.
Long story short do this:
1) On the computer with the external drive you want to use as the TM backup (the MacBook Pro here) for the other computer open System Preferences and select the "Sharing" preferences. Make sure the "File Sharing" option is turned on. Note the AFP address for connecting to this destination computer such as "afp://10.0.1.10".
2) On the computer you need to backup (the MacBook Air here). Open a Finder window and make sure none of the destination's volumes (the MacBook Pro here) are already mounted. Select "Connect to Server" in Finder's Go menu (Command k) and then enter the AFP address for the destination computer from before and connect. When the list of mountable volumes appears choose at least the destination's external drive.
3) Open TM on the computer your trying to setup (the MacBook Air) and choose "Select Disk". The external drive you just mounted should now be in the list of selectable drives for the TM backups. Then just setup the other TM options as needed.
I hope this helps. I've been trying to figure this out for about a week when I got this working yesterday. It was driving me nuts because the drives wouldn't show up on my MBP running Lion and all the posts I found for using another computer's external drive as a shared Time Machine backup location indicated it should just work. So far things appear to be working just as they did in Snow Leopard. I don't know if this is just how it needs to be done in Lion or if there's a bug in Lion. All the TM support documents I've read suggest this is a common and supported method to use TM with multiple Macs. Note that I've repeatedly ran across postings that Apple Airport Extreme Base Stations that have a connected external drive is not a supported option for using TM.
I'm not sure if all of the pondini Time Machine setup values are needed to have this working regularly, but you can check them out if needed. I've never used all of those settings in Snow Leopard or Lion and things have worked fine. I just have File Sharing turned on for the computer with the shared external drive and its been working normally.
Pondini "22. How do I set up Time Machine to a shared drive on another Mac?" link:
http://web.me.com/pondini/Time_Machine/22.html
