Place lime beans and corn in a small saucepan with enough water to cover. Bring to boiling; reduce heat. Cover and simmer for 8 to 10 minutes or until very tender. Drain, reserving cooking liquid.
Puree beans and corn through a food mill, baby food grinder, blender, or food processor, adding enough of the reserved cooking liquid until desired consistency (2 to 4 tablespoons). Use within 1 day, or freeze up to 1 month.
Spoon finished food into ice cube trays. Cover with waxed paper and freeze until firm. When ice cubes are frozen, remove cubes from tray and store in a resealable plastic freezer bag or freezer container. Label package with contents and date. Use within 1 month. Before serving, let thaw in the refrigerator overnight.
Heat thawed mixture to lukewarm in a small dish set in a pan of hot water. Stir before serving. Always sample a small bite to make sure the food is not too hot.