Lama Rinpoche is correct that the ultimate happiness of true enlightenment brings an end to suffering and death, but not in the physical body. Only the spirit can escape death and suffering which is very much a part of the material world and always will be. It is the ultimate catch 22: physical beings cannot survive without killing other beings to eat or to prevent them from eating you, but killing other beings dooms you to death by the Law of God. So only the spirit can have immortality and only the spirit and soul can know God. Nevertheless, while we are in physical form, there is much we can and should do to ultimately bring ourselves and our world to that state of ultimate happiness and enlightenment. Of course, it take many steps to reach those lofty heights, and you can't do it instantly, but you can take one step, then another and move a little closer to that goal everyday.   One small step we can take is to eat only when we are truly hungry and eat only nourishing food that supplies our bodies nutritional needs and avoid junk food that just wastes resources and the lives of plants and animals.

Note: in the above quote, “rebirth” means physical reincarnation, not spiritual rebirth.