Wash beans, and transfer beans, sugar, lemon juice, and water into a saucepan. Bring to boil, and boil uncovered for 3 minutes.
Decrease the heat to low and cover the pan, and cook the beans until very tender, adding additional water as needed, 2 1/2 - 3 hours. The beans should be very tender.
When done, there should be a total of 3 cups beans and liquid. If not enough liquid, add more water to make 3 cups total mixture. If too much water, drain some liquid.
Let the mixture cool 5 minutes. Strain the bean mixture through a sieve. Discard bean skins left in the sieve.
Refrigerate the bean mixture 2 - 3 hours until cold.
Heat the milk and cream to simmer in a saucepan.
Combine egg yolks, and sugar in a bowl, stirring with a wire whisk. Stir 1/4 cup of the hot cream/milk mixture into the egg/sugar mixture; combine well.
Transfer the egg/sugar mixture into the milk/cream mixture in the saucepan.
Place the saucepan over low heat and stir until mixture thickens somewhat, about 5 minutes. Remove from heat, add vanilla, and refrigerate 2 - 3 hours until cold.
Combine bean mixture and custard mixture and process according to your ice cream maker instructions.