Place mangos in a large stockpot and add water to cover. Bring to a boil and cook for 30 minutes. They should feel bloated and yield to pressure. Drain. When cool enough to handle, peel skins and, using knife and hands, remove as much of the pulp as you can into a bowl.
In a food processor or blender, pulse the mango pulp for about a minute, until smooth.
Put pulp and sugar in a saucepan and simmer on low, stirring occasionally with a wooden spoon. Stir in lemon or limejuice. Cook, uncovered, for 30 minutes. Let cool and refrigerate until ready to use.