If you can find some LED strips that run on 5V or actually ones that actually have a USB plug using one of those strips with a USB backup battery would probably work extremely well and be as easy to setup as plugging it into the battery.
However the vast majority of the LED strips out there run on 12v. You can buy 12v lithium battery packs but that just adds a layer of complexity plus they usually aren't that compact. So in order to make a 12v strip work with a cell phone style backup battery you would need a small step up voltage converter that can provide enough amperage to run the LED strip. Fortunately this is a thing that exists and they are actually fairly inexpensive.
https://www.amazon.com/dp/B01ID90K4A/?tag=cpf0b6-20
I can't personally speak for how well they work because I have never used one myself, but the reviews seem to be good and others are using them for this exact purpose. Just be mindful of how much current your portable battery can supply and how much your LED strip is going to draw. Depending on the density and style of emitters in the LED strip they can actually draw quite a bit of power. Also keep in mind when you bump up the voltage it automatically lowers the current so if you have a battery that supplies 5V at 2 amps once you run it through the converter you are going to probably want to keep the 12v draw under one amp or so.
I hope this helps!
