Measuring sinusoidal frequency using the common LC100-A LC meter
I expect it uses fixed frequencies, and compares voltage levels.  So, no you can't use it as a frequency meter.

I've built simple LC meters this way myself.
You generate a clean sine wave, and that goes through a known resistor and from there to the component under test and back to ground.
The voltage drop across the resistor (Node1 to Node2) and the voltage drop across the compenent being tested  (Node2 to ground) let you calculate the reactance of the part being tested, from which you can figure the L or C (since you already have the frequency.)

Ideally, you use a series resistor that approximates the expected reactance - you change the resistor for each measurement range and the frequency being used.

Like this (values are NOT representative:)







simulate this circuit &ndash; Schematic created using CircuitLab



Added note:
I had a look at the LC100 on Amazon.  The info there say it uses "around 500kHz" for normal measurements and 500Hz for "big inductances," which agrees with my assumption of fixed frequencies.

It also use 4-wire connections for the measurement, which wouldn't be needed (or even possible, I think) if measureing the frequency.