I have split the Lua discovery discussion from this topic and moved the newly created topic in a new Lua programming forum under TI programming and help:

Split topic: http://ourl.ca/10367
Lua board: http://www.omnimaga.org/index.php?board=174.0
Programming and support: http://www.omnimaga.org/index.php?board=99.0

A converter is necessary because there is a difference in voltage levels.

The Nspire is using TTL.
So you should get a USB<->TTL converter. That's the simplest way.

If you still have a DB9 plug, you can use a RS232<->TTL converter, but you'll need an additional connection to power it.
If not, you can still use it by chaining it with a USB<->RS232 converter.