In a food processor, combine the banana 1 1/2 cups of pineapple, the coconut cream, pineapple juice, 2 teaspoons of lemon juice, and the vanilla and process for about 5 minutes, until mostly smooth.
Add the remaining 1 1/2 cups pineapple and continue to process for 2 to 3 minutes more, until the mixture is very smooth and creamy. If large chunks of pineapple persist, pulse either to ten times until they break up.
Taste and add the remaining 1 teaspoon lemon juice as well as honey if you want it to be sweeter. Serve immediately.