I'd like to chime in and say that the best way of doing this is *definitely* to use a Lion-approved system, buy Lion from the App Store and then install onto the Macmini1,1 using Target Disk Mode.Thanks to the commenter who suggested that and thanks to everyone that has commented on the blog so far. I'm still going to hold off installing Lion again on my Mini until the issues I was having with waking it with the Apple Remote and using WOL are sorted out (hopefully in 10.7.1).
Once you've installed onto your Macmini1,1 internal drive, boot your other Mac (the one you've used for the install) normally and add:
to the appropriate place in /Volumes/<name of target drive>/System/Library/CoreServices/PlatformSupport.plist I would advise not deleting the file; always best to work with the software, rather than binning something it's expecting to find.
Also, ignore all the comments about the 32-bit kernel being a problem. The MacPro1,1 is a supported system which also uses the 32-bit kernel, as (I believe) does the MacMini2,1. If you're having problems, the kernel is not the issue. Make sure you're using a genuine copy of Lion which you bought from the App Store, make that one change to PlatformSupport.plist and you should be fine.
However, this probably isn't much good to you, unless you have access to another Mac to do the update on! In that case, you could always try the original method and see how you go with it. (Some commenters are saying they are finding no problems with it). As always, when trying to circumvent Apple restrictions, your mileage may vary!
I'll probably be using this new method when I install Lion again on my Mac Mini. The only problem is that In order to make it look as neat as possible in my media centre, I plastered the cables into the wall. That's going to make using it in Target Disk Mode a problem, because the power cable is stuck in the wall!
Look ma, no cables!
So it'll be a case of dragging the iMac into the living room and doing the install from there. Ah well, something for the weekend, I suppose.
Thanks again and good luck with your newly Lion-ised systems! :)