Purée 2 bananas, 2 tsp. sugar, and the lemon juice in a food processor. In a large bowl, fold purée into ice cream, leaving streaks. Freeze until firm, 3 hours.
Melt butter, brown sugar, and salt in a medium frying pan over medium-high heat. Add dates and 1/2 cup water and cook, stirring occasionally, until thickened, about 5 minutes.
Whisk cream with remaining 1 1/2 tsp. sugar and the vanilla in a bowl until soft peaks form.
Divide bread among 4 bowls. Slice remaining banana. Scoop ice cream into bowls and top with banana, dates and sauce, whipped cream, and nuts.