The surest way to know if a memory module will work is to consult the Gigabyte Memory QVL list of tested memory on their website.
It's a limited selection of tested modules, so the chances are that your module may not be in the list, but if it is, then you know for sure it will work.
The manual for the motherboard had no mention of DDR3L, and it seems out of date. The highest memory mentioned is DDR3-1333, but the board supports DDR3-1600.
You might look in the system UEFI in the memory settings, to find which memory voltages are allowed. If 1.35V is allowed, then you know that there maybe some DDR3L modules that will work.