LoL Akali Mask ( battery-powered APA102 setup )

No problem about running both off a LiPo. I do it all the time.

In fact the docs in the reference page for the neopixel library say:

Espruino devices tend to have 3.3v IO, while WS2812/etc run off of 5v. Many WS2812 will only register a logic '1' at 70% of their input voltage - so if powering them off 5v you will not
be able to send them data reliably. You can work around this by powering the LEDs off a lower voltage (for example 3.7v from a LiPo battery)

The original board itself should work fine when plugged into USB and the battery via JST. It's got circuitry in there for it, and in fact newer 'Original' boards even have pads in there to solder on a LiPo charger :)

The only one to watch out for is the Espruino WiFi. That has no JST connector and no battery switchover circuitry - so you can't just connect a battery to the power pins and plug in USB because you'll basically be shorting the battery across 5v!