In such cases, calibration of VNA is very important because you measure impedance on Smith Chart.
As I see, the Input Impedance changes its polarity between 4.3nH and 5.1nH that means the Input Impedance has a capacitive part around this point.
You compensate this capacitive part by adding inductance.
-VNA must be very well calibrated with a high quality cables and calibration set with SOLTP capability.Small amount of cable length changes too much the measured impedance.Therefore Phase Calibration is very necessary.Because cables don't have pure 50 Ohm impedance.
-If a Transmission Line is used, the Characteristic Impedance should be accurate
-Inductor value and tolerance ?? Q Factor ?
-PCB and parasitic components around IC Input and Antenna
-Does the Antenna have 50 OHM, sure ??
-Signal Processing after the LNA.. Is it so good ??
-Electromagnetic Interferences in the measurement medium that worsen BER performance
-Have you ever simulated that portion of the PCB in a planar EM simulator?? Compare with measurement results.