Peel the banana, coarsely chop, then mix with the lemon juice. Puree the banana with the milk, cream, and ice cubes in the blender. Blend strongly for several minutes until thoroughly combined.
For the garnish, cut the banana into thick slices diagonally. Place the banana slices on the rim of 4 highball glasses. Pour the shake into the glasses and let rest briefly, so that the shake can settle. Once the shakes have settled, serve immediately.