I dont think you have to even tell them?? I had medicals thru work and its your general health they need to know about. They will of course ask to weigh you etc but its of no concern to them what you eat... they wouldnt question your normal food diet so I wouldnt say anything about being on LT, its only temporary anyway and hopefully the job wont be! I would keep it quiet if it were me.. one of my medicals went back as saying I was overweight obviously but i was never questioned about it, and if I were to be I would judt say that you were doing all you can to address it.
good luck with the job xxx