Lost weight and drink solid beers? Nice! I found a post about this experience [1] which also has a few bits of research [2] linked as per your question.

One of the articles says "Water-only fasting should only be done in a specialized clinic" and "certain types of very low calorie diets, and particularly those with high protein content, can increase the incidence of gallstones in women at risk"

So perhaps the Belgian monks know what they are doing with the calories and low protein in the beers!

[1] https://www.beeradvocate.com/community/threads/monk-style-be...

[2] https://news.usc.edu/82959/diet-that-mimics-fasting-appears-... and http://www.cell.com/cell-metabolism/fulltext/S1550-4131%2815...