Q: When I upgraded to Lion, I lost access to all my Appleworks data bases. What is needed to access them?

You are not going to be happy with the answer, I'm afraid: nothing will open AppleWorks databases except AppleWorks. You will need to find a way of running AppleWorks.

You could buy an external hard disk, install Snow Leopard on it from your install disks, boot from that and run Appleworks there. It may also be possible to run AppleWorks on Snow Leopard under emulation - Yvan reported success doing this with VirtualBox - please see this thread:

https://discussions.apple.com/message/15797018#15797018

Once you can access Appleworks, you can export your databases as ASCII text and open them in other programs, though you will lose all formatting and calculation fields will being over the result, not the calculation. More info here:

http://www.wilmut.webspace.virginmedia.com/notes/aw/page5.html