Peel bananas and cut into 1 inch pieces. Hull strawberries. Place bananas and strawberries on a baking sheet. Freeze until firm.
Combine yogurt and honey. Set aside.
Add bananas and strawberries to a food processor or blender. Process until smooth.
Combine processed fruit, yogurt mixture, and lemon juice. Add to an ice cream maker and follow the manufacturer's freezing directions. Remove from ice cream maker and place in freezer safe container to cure in the freezer.
Without an Ice Cream Maker
Combine all ingredients in a blender or food processor. Process until smooth. Place in freezable container and freeze 45 minutes to 1 hour.