John Dowland, and his Lachrimae, etc. I've got a number of recordings, with the English crews including the Emma Kirkby and Anthony Rooley crowd on L'Oiseau Lyre, and some lutenists and consort music recordings.
You're very right, Monteverdi et al would be early Baroque, although within the time frame you mentioned.
I enjoy lute music so much that I had one made for me a number of years ago, and learned to play it passably. The thing about Renaissance lute music is that even simple pieces were beautifully composed.