Getting old updates for minecraft xbox edition

Is there a way to get old updates on minecraft Xbox edition? I want to be able to play the minecraft xbox version of beta 1.6.6 for a non-laggy nostalgia rush.

Not really, no. Your only options are:

• Whatever version shipped on the disc (assuming you bought a disc-based copy, delete the title updates from your system and then skip any updates)
• Whatever version you have now (assuming you haven't updated to the latest and you decline all future updates)
• Whatever version is the latest

There's no version history when it comes to Xbox Live patching of games, Minecraft included.