If you reconfigure the LC circuit, as a series resonant element,
I suspect you'll see "Resonance" as a point at/near the SmithChart
centre point, where the L and C almost cancel themselves, leaving
the resistor for the VNA to "see".? Any losses (resistance in the
inductor, or losses in the capacitor) should show as a less than
perfect 50r match at resonance.
Try it and see perhaps?
73.
Dave 'KBV