Lasix is just a diuretic. It is commonly given to people with congestive heart failure to drive out excessive liquid that promotes a "wet" cough. Both my mother and oldest son had prolonged periods of congestive heart failure. Mom was balancing a steadily degrading level of kidney function from the Lasix vs having lungs full of fluid so she couldn't breathe. The week before she passed, a lung X-ray to evaluate the "wet" state of her lungs turned up lung cancer in both lungs.
Hillary appears to be on drugs to treat Parkinson's. The coughing may be due to progressive loss of control of the throat muscles needed for proper swallowing. She will aspirate saliva and/or water into her lungs. That sets off a coughing fit.
There was once upon a time, a scandal, which I no longer recall clearly, about Race Horses being given Lasix, and its effect on their lungs.
Since elections are often coloquially referred to as horse races, I was being indirectly sarcastic.