Okay so, there was some discussion as to how this might work, and this is how it breaks down as best I can tell. The Limelight uses Raspberry Pi hardware at the core (Pi Compute Module 3), which will consume 2-4A at 5V but will run on less (if throttling is an acceptable solution when using Raspbian). The LEDs in the LL are an unknown quantity and voltage, presumed to be 12V. All the same, there’s an internal buck converter to step down the robot’s variable voltage (13ish to 6ish at worst) to 5v for the Pi. If you have stabilized 5V output already (say, from a USB Battery Bank), you can power it that way. IIRC the LL1 has a USB port for flashing, as does the LL2 and 2+.
In theory, it should be able to be powered off of it that way, meeting 2020-R33, it should be fine without LEDs. You can also combine the output of multiple USB ports for more current though, to hit a comfortable 5A@5V that the Pi inside the LL would have no problem running off of. The issue is still the LEDs, but Amazon also has 5V LEDs if you’re in that much of a pinch To go this route, please pay attention to 2020-R33-B, which would require the use of an intermediary PCB to facilitate connection using only COTS USB cables.
That said, if you can free a PDP slot and use that, that’s far and away the best route to powering it.