What is probably the largest online collection of lute music in the world is at http://gerbode.net/ (and mirrors). There are currently more than 3,000 pieces available (actually, I think it may be closer to 4,000 by now), many in several different arrangements. All of them are available in Fronimo file format, and most of them are also available in TAB, PDF, and MIDI.
You mentioned Dowland. A quick glance shows more than 100 pieces by him alone. There are 588 Fronimo files under his directory, including separated parts for SATB singers.
The collection is entirely free -- both in price and in copyright. All of the pieces are transcriptions by Sarge Gerbode, either from the originals or scans of the originals made available to him by libraries. This collection represents many years of work by him and it has been a labor of love. I'm currently working with Sarge to put a much nicer front end on the collection and we hope to have the up and running by Summer, if not sooner.
Check out the site. You can contact him at email@example.com, or me at firstname.lastname@example.org.