I checked your registered products and your seats of AutoCAD LT 2011 have been upgraded to the 2012 version. This means that you now have two options:
1. Install and register the 2012 version normally.
2. Try to activate the product normally on your second computer. If you get an error, please Private Message me (envelope up there by your username) the serial number and request code for the 2011 product you need to activate and I'll do it manually for you.
If you decide to go for the second option, please send me the information via Private Message as mentioned above, do not post it in the public forums for security reasons