I do not see the name of the person asking the question here in this posting - but using simpler logic than Peter used above I will say:
Normally when we clean out a well or Drill a Shoe track or hmmmmm what else can we be doing before we need to do a LOT/FIT or what was it Peter XFIT?
I would say in nearly all cases we pump down our DP or Tbg or what ever we have for a Work String to do the cleaning of the well bore prior to an FIT
We would also want to have the Fluid In SG/PPG and Fluid Out a very similar Value - We will be able to measure & know very well the Fluid SG we put into the well and be able to calculate the Hydrostatic pressure this Fluid will create.
So I would think that the practical method would be:
1) Circulate the Work String & Annulus until they are close to same weight of Fluid.
2) SI the BOP on the Work string & begin a Physically measured volume, low rate of pressure build up pumping down the Work String (some areas & Rigs have a Special Pump about the size of your Triplex Accumulator pump so to assure a small & consistent volume per minute) - this pressure up will be monitored on a freshly Calibrated or Dead Weight tested Chart recorder.
3) Monitor the Pressure BU on the Annulus (with a Second Chart Recorder if available) to be able to compare (in the end) Clean Fluid with Dirty Fluid effect on the Hydrostatic - (at least 1 DWTested Chart Recorder or Pre-calibrated Pressure Gauge double checking the Main Chart Recorder & pressure gauges on the Pump/Work String.
My mind goes to the usually smaller volume of the Work String & the normally cleaner (more pure) Fluid leaving surface right from the Rig Tanks to pump to standpipe to pipe in the well - which normally will have been happening for some time (maybe even several hours). I would think we should feel more comfortable that we have a cleaner environment by using the Work string for the LOT volume wise on the whole well it should be very much the same forward or reverse (RH or LH).
The cleaner Fluid should also give a more pure answer than Annular Fluid being pumped towards the Formation of interest.
Depending on the area and the formations needing the FIT we could also be looking at displacing the work string to water & over displacing the heavier fluid on the back side to ensure cleanest possible fluid into the Formation of interest - but this would be more complicated & not necessary in most cases one would think. . .
Best Regards & Wishes