You can indeed update without live, it's a bit involved but not too hard once you do it.
You'll need a couple things:
1. A USB thumb drive
2. Horizon (www.xboxmb.com/horizon/)
4. A Brain
First you gotta format the thumb drive for the xbox. Plug it into your xbox and start her up. Then go to: My Xbox>System Settings>Memory
You should see your thumb drive listed, you must format it so it will be usable by the xbox. You will lose any data on it. You should be able to just hit A to format it, or you might have to hit Y and select it from an option.
Second, go to the update site: www.xbuc.net . Find your correct title (notice the NTSCU/PAL and select the right one according to your game. NTSCU is North America, PAL is Europe, you can google any of those codes to find out) and download the latest update for that title. Remember where you save it!
Third, Plug your USB drive into your PC. Start up horizon, it will try to connect to a server to check for updates and news...we don't care about any of that stuff. What you want to do is click on where it says tools in the program up top. Then you want to click on package manager and then Open. Navigate to the title update you downloaded earlier (you remember where it is right???) You will see the games logo pop up with the title update that you load so make sure it's the right one.
Fourth, Click save to Device and select your thumb drive. Close Horizon and safely eject your thumb drive from your PC, plug that bad boy back into your xbox.
Finally, you can go 2 routes here. You can either leave the update on your thumb drive and plug it in every time you want to play that game to have the update....OR a better option is to transfer the file to your xbox Hard Drive. You can transfer it by going to system settings>memory>then select your thumb drive. Navigate to the games folder and you will see the title update for your game. Press Y for more options, then select Move. Now you can keep it on your HD and not worry about having the thumb drive in.
Hope it helps! A new Skyrim update was released today actually.