Ok I finally got Migration Assistant to work, transferring from MacBook Pro running OS X 10.6.8, to new MacBook Air running Lion 10.7.
I ran software update on the MacBook Pro. I then also manually installed the patch/update for the 10.6.8 Migration Assistant, which allows it to interface with Lion machines:
http://support.apple.com/kb/DL1420
(Why does this not get installed automatically when running the software update...)
I then went into System Preferences on both machines.
Under Security I turned off the firewall.
At this point I tried to use Migration Assistant, with the computers connected by ethernet cable - and got the "looking for other computers" message on both machines.
I went back into System Preferences on both machines.
Under Sharing, I checked the box Internet Sharing - and ignored the dire warnings how my ISP would cut me off etc. and activated this.
I then restarted Migration Assistant on both machines, and was able to run it no problem.
Hope this helps as it took me a couple of hours of messing around to figure this out...
Once Migration Assistant has finished, you should go back into Sharing and uncheck the Internet Sharing boxes on both machines.