LIFO is seen as fair by those on top of the seniority list because it would safeguard them at the expense of their younger colleagues. Conversely, those on the wrong part of the list usually have different views, often along the lines of "why me, having 30 years of working life ahead, instead of someone having 3 years of working life left".
Whatever you do in such a situation, someone will be upset with it. There's no nice, non-discriminatory way of showing someone the door, especially in a situation when they are unlikely to find a comparable job anytime soon. Except for the case when the entire company has gone belly-up and everyone is in the same boat, someone will inevitably suffer more than someone else.