That's not a complete diagram, as you haven't drawn the data and clock connections for the APA102 LEDs. If you have those connected directly to the Attiny85, you'll have to be mighty careful because:
If you take the gate of the MOSFET low, the MOSFET switches off, so the drain voltage of the MOSFET rises to the (say) 4.2V from the LiPo. This is correct, it's what you want, because that means that both the VCC and GND of the APA102 are at (say) 4.2V, so there's zero volts
across the APA102, i.e., it's off.
However, if you were to make a software mistake, and program the attiny to make it output a '0' on the clock line, that would mean you had:
APA102 VCC: 4.2V
APA102 GND: 4.2V
APA102 CI: 0V
In other words, from the APA102's point of view, you'd be applying
negative 4.2V to the CI pin. This is in excess of the limits of the datasheet, and could cause damage, or the LEDs would try to power themselves via the protection diodes in the APA102. The same goes for the DI pin as well.
So it'll work fine, but you have to be absolutely sure that your code leaves the DI and CI pins either high or floating before switching the MOSFET off.
If this seems confusing, you might consider using a P-channel MOSFET to switch off the supply to the APA102, rather than using an N-channel MOSFET to switch off the ground connection. This might be a bit easier to understand, although you still have to be 100% sure that if the MOSFET is switched off, you must have the DI and CI pins either
low or floating.
Don't disconnect it from ground, disconnect it from power. Then you don't have to worry about the data lines providing a path to ground in the off state.
Correct, except if you disconnect the power, you have to be equally worried about the datalines providing a path to VCC in the off state, it's exactly the same problem. It's just easier to intuitively understand the risk if you disconnect from power.