OK, so the procedure of reading the LMT01 is:
- use a resistor to convert the changing current of the sensor to a voltage you can measure
- use a comparator to generate
- apply power to the LMT01
- wait for the first rising flank and start counting
- after the first rising flank, count fort at most 50ms
- after the 50ms are over, stop counting and power off the sensor
So, first I think you should route the output of your comparator to a pin an connect a scope there (together with looking at the LMT01 current consumption). Make sure the comparator delivers a usable result.
Since the pulse frequency is up to 94kHz, your comparator needs to be clocked at least twice that, preferrably much more than that (I would suggest using a 1MHz clock or faster). Same for the counter.
The counter for your pulse is wired fine. For measuring the 50ms I would use a second counter, which gets configured to start counting on a rising flank. It should have its TC count so that TC is reached after 50ms, and you use this to capture the pulse counter result, and trigger an interrupt to read the results.