I don’t know anything about the Malibu LED light system and it’s not clear to me which irrigation controller you’re trying to use. But… This sounds like a simple matter of looking at the power requirements of the LED light system and matching it to the output capabilities of the irrigation controller. Assuming you’re trying to power the lights directly from the controller, some basic questions need to be answered: What voltage is required by the lights? Sounds like 12V. Is that 12V AC or DC? What is the amperage required by the lights? Once you have those questions answered, then you can compare to the output of the irrigation controller. Is it outputting the right number of volts in either AC or DC that the lights require? Will it be able to supply the needed number of amps? You should be able to find out this information by looking at the specs for the lights and comparing to the specs for the controller.
If the controller isn’t outputting the right voltage or can’t supply the amperage needed then you’d probably be looking at having the controller control some sort of switch which turns the LEDs on/off instead of controlling them directly.