It all depends on how the LED (with resistor) is connected...
Direct picaxe connection:
a) Connection between picaxe and +V will require a LOW 1 to turn the LED on.
However, if you're using a project board which has a darlington driver, then the output will be inverted, so the following applies...
Darlington driver output:
b) Connection between darlington driver output and +V will require a HIGH 1 to turn the LED on.