I think I've figured out what caused the step in S21 that I mentioned in my previous log.

The LiteVNA uses two different oscillators to drive the DUT, called LO and HI, with LO being used below 100 MHz and HI above. It turns out the drive strengths of these two oscillators is slightly different. This alone isn't an issue, but it also turns out that the default drive strength is such that the LNA output is driven pretty hard in my set-up. I suspect this puts the LNA in a (non-linear) region where gain depends on drive strength, hence the step in S21.

Happily the drive strength can be adjusted, and if I reduce the drive for both LO and HI (to minimum) then the step in S21 disappears: