Is your Lithium pack LiFeP04? Odds are the lithium pack is not 12V, it is 12.8, or maybe 11.1, depending on the chemistry of the battery. If you don't know, then there is no way you can do it.
Some LED supplies, Meanwell comes to mind, allow you to adjust the max voltage (and current) and indeed you can use them as a battery charger. Would I do that for cobalt electrode Lithium Ion? .. not a chance, they are too sensitive. I would do it in a pinch for LiFeP04
Sounds like you need a charging control unit sitting in between the LED driver and the battery. No matter it is a constant voltage or a constant current LED driver, it is a pretty straight forward "dump" power supply. It has no way to know what the charging voltage / current suitable to apply to the battery for each specific moment. If there is no protection built on the battery, you are running high risk of over-charging the battery.
I've heard people using icharger device (or unit which has similar functions) as the charging control unit, but have never got the chance to actually try it out. You can google the device to see how the charging control unit can help you.