I'm surprised that, based on the OP, people start having visions of the worst-case scenario, requiring doctors, nurses, vomiting, cardiac arrest, late-term pregnancy/premature birth etc. All the stuff you see on these 911-type reality TV shows. I think we all agree that something like that is best left to the specialists, if necessary in an ambulance-type aircraft with sufficient space for one or two pilots, a stretcher with the patient on it, and a doctor/nurse to perform whatever medical duties need to be performed. I also think there's a special medivac thing you can put in the flightplan for such flights, giving you priority in some cases. And these patients, upon arrival in a hospital, are not going to be moved anymore unless to a better equipped hospital.
But as far as I see it, the OP was asking about a situation with a patient having a chronic disease, would die rather soon, but was not expected to need immediate or continuous medical attention during the flight. Altogether a different situation, and a situation I find myself in every now and then.
My flying club has a number of charity events around the year where we take chronically ill or handicapped children up for a pleasure flight. They are, in their normal life, under regular control by a doctor, but are out of the hospital and there's no above-normal chance that their condition will all of a sudden worsen during the flight. We're talking physically or mentally handicapped children here, or chronic diseases like cancer.
We typically offer them a local pleasure flight of about 25 minutes, as part of a larger program. The route is chosen so that if the need should arise, we can announce a mayday and be on the ground in, say, five to ten minutes. For big events where we take multiple patients up in multiple flights, we inform ATC and the airport authorities beforehand, agree on routes, callsigns etc.
In each and every case, the patient has been signed out of the hospital by a doctor and in most cases we specifically ask the parents to check with the hospital to make sure the doctor doesn't see any objection to the flight. During the day itself we make a point of not discussing the disease with the patient, but we do have an agreement that certain types of diseases always require a parent or other responsible adult to accompany the child (lung diseases requiring the continuous use of oxygen for instance) or that the patient sits in the back, unable to reach the controls (mental illness, epilepsy).
So... As long as the patient has been discharged from hospital, and you have consulted with a doctor or other specialist to determine the specific patients disease and the effect it might have on the safety of the flight, I think you should be fine from a flight safety standpoint.
Should he die enroute you could theoretically be sued by the family for the death even if they gave consent?
You can be sued for anything. Question should be: Can you be convicted? Now in this particular case, everyone knew his death was imminent and there was nothing the medical establishment could do about it anymore. If he were to die in your aircraft, have you been negligent enough to get convicted for that? Ask yourself: if he were to die in your house, would you as the homeowner be responsible? If he were to die on a public street, would the government be responsible? I think if you would have talked things over with a doctor, and the doctor agreed that the flight would not make his medical condition any worse than it was (thus not increasing the chances of dying above what they were) you should not have a problem at all.
Some of the other problems would remain though. Obviously the patient should not in any way be able to decrease flight safety. Obviously you are going to plan your route more carefully, keeping a list of alternates with medical facilities to hand.
One last thought: There may be a legal problem in transporting somebody with a contagious disease from one country to another, regardless of whether the contagious disease is responsible for his condition or not. I don't think this would be relevant to your specific case, but it might be something to think about in another situation. I know a lot of hospitals will only accept patients who have been hospitalized in another country after a three-week quarantine period because of MRSA.