https://cryptostocks.com/ has been around for a while and was originally a Bitcoin exchange.
https://www.litecoinglobal.com/ Is fairly new and solely intended for Litecoin. I think LitecoinGlobal will be the best bet because Litecoin is their only focus, but I'm going to leave it up to you. Whichever gets the most votes here will determine what we do.
Either way, I look forward to establishing Cognitive-LTC.
-Garrett
EDIT:
If GLBSE fully supports LTC within the duration of this poll, we will use GLBSE.
Update:
Main Cognitive-LTC thread is here:
http://forum.litecoin.net/index.php/topic,568.0.html