You can use mixed mode s-parameters to have a full linear characterization of the LNA.
There is a lot of literature about mixed mode S-parameters (google it), I'm giving you just a glance about them:
Your device is a 3 port device ( ports are: in, outp, outn) that can be represented as a 3 port device (ports are: in,out_diff, out_comm) without any loss of information.
You need first to measure the S3P matrix (in, outp and outn). If you have a 4 port VNA this is straightforward, if you don't have it you can measure the 2 S2P files (in, outp, with outn terminated with 50 Ohm) and (in, outn, with outp terminated with 50 ohm). Then you have to combine the two 2X2 matrix to obtain a 3X3 matrix.
Now you've got the S3P file.
Apply mixed mode transform and obtain a new S3P file in which you'll have, for example Sd1 as the gain of the LNA, Sc1 as the common mode rejection, Sdd from which you can calculate the differential output impedance and so on. Use a simulator like Agilent ADS or a similar one, or matlab, or mathcad, or whatever you prefer, you just need to know the equations behind that.
Be aware that you need to measure the S-parameters with input level well below the P1dB (at least 10 dB below) of the LNA, remember you need to be in the linear region.
I hope it can help.
Mazz