Drive the L port with appropriate power level during the measurements of R & I ports!
Typical values for L power are +10 dBm.
Of course use CW signal, and prefere a spurious "clean" generator. Harmonics are not important, since they are generated in any manner inside the mixer.
If you want measure sii at L port, check, with a power meter, if your VNA is able to deliver enough power, some agilent 872x and Anritsu 37xxx can do it. Then, close the other 2 port into matched load and
A little suggestion. When measure sii at R & I ports, be sure that the generator is well matched, or place a ferrite isolator or an attenuator across the L port.
Enjoy with the measurement rather than chat