Dear Edisraw,
Sorry to hear of your dad's problems. It's a great thing that you even consider offering him a liver lobe. I imagine that it will mean a lot to him just knowing that you care that much.
As you are jusy starting to look into this you will have a lot to read and learn. If you click the section on living liner donation at the home page of this site you will find a lot of information about the requirements and testing involved.
First of all, as you mentioned, you will need to find out a lot more about your Dad's condition. Liver transplant is not a treatment for all types of liver diseases. And not all patients who need a liver transplant meet the requirements to indicate that could successfully receive a transplant. If the doctors decide that he both needs a transplant and is able to receive one safely he would be put on the list for a transplant from a deceased donor. In some parts of the country the wait is longer, in other parts it is shorter.
To become a living liver-lobe donor a person has to be in good health (so as to be able to safely undergo the surgery, and safely live with only a liver portion until it grows larger.) Overweight and some of the other problems you mention might be judged to be obstacles to living donation. Living liver donation is also stressful on the psychological level, so the potential donor's mental health and history have to be considered. All in all the doctors will not operate on a donor unless they are reasonably confident that he/she can handle the surgey and recovery well: physically, mentally and economically. And of course the actual health and condition of the liver has to be carefully examined.
So, keep reading up on the topic and get yourself well informed. But from what I have read from other liver donors it looks like you would have a number of obstacles.
But it might be that this experience can be another motivation to take better care of your own health in the future, both for your own sake and to be better avle to help your Dad and others.
Hope some of this info helps. I myself am a kidney donor, so I'm just passing along what I have learned here and there about liver donation.
best wishes,
Fr. Pat