VNAs work with a "reflection bridge", and require calibration to short, open, and 50 ohms with well-known standards.
LCR meters do a phase-sensitive measurement of the voltage and current on and through the unknown and compute the relevant parameters from those data.
They require only a short and open calibration, with no important transmission-line effects at relatively low frequencies.
Especially when measuring extreme cases (high C and low C for this case), a fresh calibration is needed for both types of units.