Hi. Can you post a photo of your lute? It would be very unusual to have the first 6 strings as singles -- normally just the first string is single. And, there should be an odd number of pegs: 10 on one side and 9 on the other would be normal for a 10-course lute. As for tuning, I doubt if your memory serves you well: a lute should not have ever been tuned like a guitar, nor would you have needed to adjust the third string for some Dowland pieces (that is a guitar thing). If your lute is a 10-course Renaissance lute, normal tuning would be (from single highest string): G, D, A, F, C, G, F, D#, D, C.
There are two places (online) where I have bought lute strings: Aquila usa, and strings by mail. If you contact Aquila and provide some information about your lute, they can help you determine what strings you need.