Hans,
Let me ask the question a different way. Is the issue that you want to know how to measure the s-parameters of a differential circuit? That topic is discussed in
http://www.designers-guide.com/Analysis/diff-sp.pdf. Or, is the issue that you want to know how to measure s-parameters when there is no obvious resistive load? I don't think I know the answer to that one. It's not clear that s-parameters make much sense in that situation. That is why I asked why you want the s-parameters.
If you are determined to compute the s-parameters, you might consider building a matching network that fits between the LNA and the load port that to the LNA exhibits the impedance of the mixer.
Alternatively, you can build a model for the load that looks like the mixer, and then sample the output of the LNA using a VCVS and use that to drive the load port. In this case, of course, S22 and S12 are meaningless.
-Ken