If you can get gamertag from live id API, you can use this :
Small http://avatar.xboxlive.com/avatar/sample/avatarpic-s.png
Large http://avatar.xboxlive.com/avatar/sample/avatarpic-l.png
Full body http://avatar.xboxlive.com/avatar/sample/avatar-body.png
Of course, you have to replace "sample" with a gamertag.