Yup, Lightroom 1.3.1 works on Vista.
I couldn't open CS3 on Vista until I discovered turning off my User Account allowed CS3 to work. Go to Control Panel>User Accounts>Turn User Account Control On/Off>untick the box and click OK.
Every time you open Vista, you will get a message on the bottom right of your screen alerting you that User Account needs your attentioion. Ignore it.
Whenever I retick the user box, CS3 won't open.
Try it anyway - it worked for me. Perhaps it's something Adobe should have a look at.