1. Peel sweet potatoes and banana; cut into 1-inch chunks.
2. In a 3- to 4-quart pan, combine sweet potatoes, banana, and milk. Split vanilla bean in half lengthwise; scrape seeds into pan, then add pod (if using vanilla extract, add it later). Bring mixture to a boil over high heat, then reduce heat, cover, and simmer until sweet potatoes are tender when pierced, 11 to 13 minutes. Remove vanilla pod and discard.
3. Pour sweet potato mixture into a fine strainer set over a bowl; discard milk. In a food processor, purée sweet potato mixture with butter (and vanilla extract if using) until smooth. Stir in lemon juice and salt to taste. Spoon into a bowl.