At 5'7" 140-145 a 144 day fast is not necessary I think. I am by no means an expert in this matter but that is too long.
On average you might lose 1-.5 pounds per day is a Water Fast and a little more if dry. So at a rough estimate your basal metabolism is 1400 so conservatively 3-5 pounds per week. You could consider maybe a combination of juice, then water and a few dry days then back to water and then refeed. Or consider intermittent fasting with one day eat one day fast one day eat etc.
If you have not fasted before why not try a 2 week juice fast to see what it does for you and then decide from there?