When using LUNA in Apollo mode all inserts that don't run on Apollo'S DSP get bypassed while in record. If you understand how near-zero latency works in LUNA, it makes perfect sense. All the processing (and monitoring) is done on the Apollo. For your EZMix, the audio would need to travel to the computer and then would need to be fed back into the CUE system, which brings additional latency.
You have two possibilities: switch to Core Audio to record your guitars using EZMix, or use a standalone instance of EZMix (don't know if there is a standalone version of it) and route it to LUNA through a Virtual Channel