You're partly in luck--I just went through a listing of all Dowland's lute music and there are only four works with the name fantasie or fancy. They are, with the corresponding Poulton numbers:
A Fancy P6
A Fancy, P7
I don't have the sheet music but I think the Poulton numbers will help with your search.
(US) (GER) The greatest good you can do for another is not just share your riches, but to reveal to him his own - Disraeli