If it is an 11.1v lipo (also known as 3s), that would be a 3 cell lipo, not just one as you mentioned above. Lipo cells have a nominal voltage of 3.7 volts. So 3 x 3.7 = 11.1 volts, which is what you mentioned you have. So yes, they need to be balanced. The 3 cells internally, in the single pack, need to be balanced with each other.
I don't mean this to sound harsh at all, so please don't take it that way, but when someone has little experience with lipo batteries is when these kind of bad things happen. That is not meant to be critical, but more of a fact. As I have mentioned, I have been into rc for years, and for the most part, inexperienced users are the ones that run into issues. That isn't to say that occasionally there is a bad cell, bad charger, etc, but for the most part, inexperience is the issue. As I said, your 11.1v lipo isn't a "one cell lipo". If it is by chance, then it is new technology.
I'm sure this can be backed up by other experienced lipo guys on this board like Nec and slipstream too.