I think most use a USB thumb drive with Lion Recovery Assistant. but the web page says it can be used on an external drive too. Are you sure your current install of Lion has the Recovery HD present and it's not corrupted?
The Lion Recovery Assistant needs to have the built-in Recovery HD partition available. Open Utilities/Terminal and type diskutil list. Check to be sure the Apple_Recovery HD partition (~650mb) is there. If it's not or it's corrupted, you will need to recreate it by reinstalling Lion on top of itself then reapply the 10.7.1 update.