Can't say exactly why the lights aren't working, but it could very well be because the rest of the electrical is dead.
So, your battery won't hold a charge. Is this a wet cell or an AGM? If its a wet cell, are the electrolytes still in the battery? Do you have a bad cell? If AGM, the battery is probably toast
More bad news...If your bike starts on the jump pack, but shortly dies afterwards, your charging system is probably toast as well. There's a chance a really screwed up battery could be inhibiting the flow of electrons, but typically even if you have a dead battery, if you can get it started, the charging system should keep it running.
So, what I'd do:
Step 1: take some measurements of the battery. If its at 9v or 10v, its probably toast. If it is 11v or better, put it on the trickle charger for a bit, and measure the voltage again and see what you get. Around 13v? Thats a good sign. If you get a good voltage after charging, try starting the bike with just the battery 2 or 3 times, and check the voltage again. Is it below 12v again? Probably toast, can't hold a charge
Step 2: replace the battery. Go with an AGM battery
Step 3: Start the bike. let it warm up, and rev it up to 3000 RPM or so and check the voltage while running at 3000 RPM. Are you getting 13.5v+? If so, thats a good sign. Try 6000 RPM. Closer to 14v now? Good. If its around 12.8v or so, your charging system is dead.
Try some of these things and report back. If your charging system is dead, we can go from there