General Pilates
Warlord
Everything I've ever seen about the early Spartan state has indicated that it had either a very small (in terms of value, at least) treasury or a nonexistent one, and did not seriously employ monetary levies. The buildings required to store a treasury of any appreciable monetary value when employing iron coinage would be...uh...prohibitive, to say the least. They didn't maintain a facility at Delphoi like most of the other poleis of import, either.
Sparta itself never maintained or supported a "sizable navy" in a meaningful sense, even during the hegemony, as already noted, but if the Spartans did have to disburse funds for the use of "allied" ships, I would imagine that they would not use their own currency, because nobody else wanted anything to do with it. Sparta acquired a fair amount of legit cash in the form of Attic talents and other hard currency from the campaigns in Aegean after 413 (admittedly, this comes secondhand from Grote because I have no alternative at the moment and suck at classics) and they may have used this money, but that still gives us a chicken-and-egg problem and I don't know if anybody's resolved it yet.
Hope that helps; it probably doesn't.
Sparta's own navy was complete non-existent. Nearly all of the navy of the Peloponnesians was the contributions of such states as Corinth.The Spartan treasury itself didn't exist until after the Pelopennesian war. Even then it was just used to build temples and the like.
Now, as a person studying Persia quite fervently, I'll take any questions from people about it. Any era is fine.