This already works as you described, and I have mine set up that way. Create a custom field in the Assets section of setup. Then go to Discovery Connections, click Lansweeper, and your custom field will appear at the bottom with a drop-down of Lansweeper attributes. Select one of the Custom1-Custom20 attributes. You will need to check in Lansweeper to see which custom attribute number you use for the Asset Number.
I had just missed the Asset Custom Fields in WHD! D'oh!
Cheers for pointing that out. I will try it out now.