Which front and rear lights can run while charging? I have a 52V battery pack on my krampus, which I use for commuting to work.  I plan on buying a DC-DC converter with two USB outputs to run headlight and taillight.  So my requirements are mostly to be seen, with flash and bright enough for city nights.  Any recommendations are very appreciated since documentation doesn't include the ability to light WHILE charging.  It might turn out  that I am forced to go with a dynamo style system substituting my battery pack and the converter for the Dynamo hub.
ps. On a budget.
Update: thanks for all the help everyone.
I decided to avoid the step-down dc/dc converter and  go with purchasing these...
***update 2: I improved things further with this new link; A bit expensive but the optical quality is high with sharp cut off. Perfect solution for direct-pack lighting.
https://www.ebikes.ca/shop/electric-bicycle-parts/lights/roxim-x4-ebike-light.html
https://www.ebikes.ca/shop/electric-bicycle-parts/lights/led8rb-jk.html
USB rechargeable lights are not typically designed to be run off of USB power continuously, they're only designed to be charged over USB. I run The Bike Light Database, and have tested dozens of different USB rechargeable lights. A few models will run while plugged in, but typically do not charge if turned on, and only run at the lowest output setting. 

If you're already going to be getting a DC-DC converter, you would be better off getting a headlight that runs directly off of DC power. It'll be cheaper than getting a battery-powered light which you don't intend to use the battery of, and probably more reliable. 

There are hundreds of options for super cheap (both in cost and quality) bike headlights which run on 8.4 V. You can probably find one without a battery pack, or if you do buy one with a battery pack make sure to recycle the batteries because they tend to be unsafe and low quality. You could also look into higher quality lights which use an external power source; many different manufacturers sell them and they pretty much all take a 2.5x5mm DC barrel plug at a nominal 8.4 V. The Fenix BT20 is a good example of one such light. 

Cheap generic Cree U2 light (left), Fenix BT20 (right)

 

It's going to be harder with taillights. I don't know of any taillights which operate when plugged in to USB, and I also don't know of any affordable taillights designed to run off of an external power supply. Your best bet might be to look for a taillight meant for vehicle usage and get a DC-DC converter which will put out 12 V. Trailer lights can be gotten for cheap online, or if you wanted something more visibility-oriented you could get a light like the type found on tow trucks and emergency vehicles. I did that using a 12V battery pack and a TIR3 light I got online and wired up: