Reasonable Li-Po Battery Protection Circuit?
Your battery is drawn upside down in the schematic, so that's a problem.

The 200\$\Omega\$ resistor in series with VCC to the ATtiny will cause a large drop in the VCC voltage when the LED is illuminated...remember that the LED current must go through R1 as well.

I'm assuming that the LED is a small red LED requiring about 10mA. If that's not the case provide a link to the data sheet. I'm also assuming that the load is resistive and does not require much current...provide more information if that's not the case.