Hi,
I have checked the LPTMR module of K66, it does not have capture function, so it is not suitable for your application.
I suggest you use TPM or FTM modules to test the signal duty cycle or cycle time. You can connect the tested signal to the TPM_CHx pin(capture signal), when the rising/falling edge of the capture signal is detected, the current counter value is loaded into _CnV register, and interrupt is fired. Secondly, the TPM and FTM have high driving clock, so you can get high resolution. The LPTMR module is designed to work in low power mode, so it's driving clock is lowerer than that of TPM/FTM, so resolution is lower, btw, it does not support capture function.
I suggest you download SDK from the link:
https://mcuxpresso.nxp.com/en/select
In the SDK, there is input_capture example, located at:
............\driver_examples\ftm\input_capture
Hope it can help you
BR
XiangJun Rong