Hi,
Yes, I agree that any exercise will help her lose weight & get fitter, but I wouldn't personally do much normal lunging. I instead play with the horse in an arena or large yard(round or otherwise), pref. free rather than on line. Hill work is another good exercise. If at all possible I would also keep the horse on a track setup, for a bit of constant exercise regardless of whether I can get there to give her some or not. You can google 'paddock paradise' for more info & ideas on that.
Lunging is hard on a horse's joints, particularly if it's on the average size circle & they are much overweight &/or unfit. You can minimise this by lunging in very large circles and, as you would need to, with a fat, unfit horse, start small & build up to any length of time gradually. Also change directions frequently and I would be hesitant to do much cantering.
Mentally, conventional lunging is generally extremely boring for the horse. So it tends to cause them to 'switch off' & start ignoring you &/or playing up, doing - or attempting to do their own thing, losing 'respect' for you & desire to do as you ask & to be with you. Keeping sessions short, chopping & changing gait & direction frequently & not being too repetitive or predictable, including obstacles and going places while lunging - eg go for a walk(pref on a hill) with her lunging around you, rather than stand in one place - will all help avoid these negative effects.