If you want some sort of ...

If you want some sort of routine analysis to do, I suppose one could use conductivity for the Lithium Bromide brine, or perhaps a dilution test.  Ion specific electrode might be able to get you in the ball park as well.  Analysis for contaminant ions is obviously somewhat more involved, but can be done, assuming the primary ion interference to the method is minimized.  Another simple test to see if concentrations are correct in the various sections are correct would be specific gravity testing.