Bring 1 cup cream, half and half and sugar to simmer in heavy medium saucepan, stirring occasionally. Whisk yolks in medium bowl.
Whisk in hot cream mixture. Return mix to saucepan and stir over medium low heat until custard thickens and coats spoon (about 5 minutes); do not boil. Strain into large bowl. Add white chocolate; whisk until well blended.
Mix in remaining 2 cups cream. Refrigerate until cold. Peel and slice bananas. Puree bananas with lemon juice. Mix puree into custard. Transfer custard to ice cream maker and process according to manufacturer's instructions.