Accepted answer
Start with the arithmetic, because the answer to the practical question is usually a number and the number is usually achievable.
DEXA precision is better than people assume for fat mass and worse than people assume for lean mass in a single scan — the least significant change for regional lean mass on a well-maintained scanner is on the order of a few per cent. That means two scans three months apart can differ without anything having happened, and it means a scan sequence needs to be at least three points before a trend is interpretable.
Worth being precise here: the first four weeks of loss is substantially fluid and glycogen. Each gram of stored glycogen carries roughly three grams of water, and total glycogen is on the order of 400 to 500 g, so the obligatory water shift alone accounts for a couple of kilograms. This is why the first month looks dramatic and the second looks like a plateau when in fact the fat-loss rate has not changed.
The evidence for a higher protein intake preserving lean mass during an energy deficit is reasonably strong in resistance-trained populations and weaker in sedentary ones, with the meta-analytic estimates supporting intakes in the region of 1.6 g/kg over lower intakes when training is present[1].
One qualification: none of this is a clinical assessment, and unexplained loss of function rather than of mass is a reason to see someone rather than to adjust a programme.
The plateau is arithmetic. Treat it as arithmetic and the response follows.