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When I said they (lion) fully charged I meant it could be & stored safely fully charged, unlike lipo's that will puff & ruin being stored fully charged.
Chances are its not a 3s 11.1v lipo. Or it would have 2 leads & 3 more small ones for a balance lead with plug. Its more than likely a lithium ion battery or similar chemistry with similar voltage to the 3s lipo. 3.3v x 3 is 9.9v fully charged its 10.9v & the 3.6v x 3 is 10.8v so 11.8v fully charged, so that is probably what it is. They typically have less voltage than lipo batteries (3.3v - 3.6v instead of lipo at 3.7v) & can be stored fully charged & fully discharged unlike lipo's & are more user friendly. So if you can find a lion battery around the same voltage you should be good using it & charging it the same way it was charged before.