Detecting when a LiPo battery connected trough a step-up board has low power.

I'd include the resistor, something like 1k to 10k is fine, just to prevent the risk of accidental short(*) on the traces of the Arduino
grounding the LiPo - massive currents would then flow, vaporising pcb traces. LiPo's can put out 50 to 100A or more if abused...

(*) Accidentally put the board down on top of something metal for instance.