Upgrading an old mac mini intel 1.1 for Lion
Short answer: No, it will not work. 

Long answer: Lion requires a 64bit processor and the Yonah processor on the mini1,1 still is partially 32 bit. You will NOT be able to boot in to Lion because you cannot boot a 64 bit kernel. However, it is possible to use a separate disk to boot into a custom boot loader and then load Lion from there (much like trying to get a MacPro1,1 to boot Lion). This is a definite hack, and not something I would recommend to anyone, especially for a super-low-end machine like this mini. It will not be happy.

Also, this machine has a SATA-I interface, so even with an SSD in it, it will still be slow.