"When I go on Xbox Live my network connection lags and I routinely get booted from live play. Is there anything I can do to stop my Xbox lagging?"
There's nothing worse than playing an Xbox Live match only to have network lag cause your character to get shot without having any control over it. Lagging network connections are typically caused by some kind of performance bottleneck in the connection, most frequently because your wireless network connection drops out periodically. Here are a few things that might help improve the situation.
If you are on satellite broadband or using an DSL provider with less than 256 kbps down, there's very little you can do about Xbox Live gaming lag short of upgrading your broadband ISP service.
Before you do anything drastic, make sure something else on your network isn't taking up bandwidth. If you are downloading movies from BitTorrent while you are gaming, turn it off. Seeding other computers can create a performance bottleneck for your gaming especially if that's also happening over wireless. While far less likely, streaming music from Pandora or Last.fm can also impact network performance. If someone else in the house is streaming a Netflix movie while you are gaming, that would definitely be a cause of potential lag.
If nothing else is using bandwidth, then the problem is more likely caused by wireless interference. It's almost impossible to completely eliminate interference, so the best solution is to switch from a wireless internet connection to a wired connection. This either means running an Ethernet cable from your Xbox to the router in your house or using Ethernet over Powerline adapters. Either solution will greatly improve network performance over using wireless.