Blanch the rapini it in boiling water for about 3-4 minutes or until it becomes vibrant green and tender. After blanching, immediately transfer the rapini to an ice water bath to stop the cooking process. Drain well.
In a dry skillet, toast the almonds or pine nuts over medium heat until they are lightly golden and fragrant. Keep an eye on them, as they can burn quickly. Remove from heat and let them cool.
Squeeze any excess water from the blanched rapini. In a food processor, combine the blanched rapini, toasted nuts, peeled garlic cloves, and parmesan. Pulse the ingredients in the food processor until they are finely chopped and well combined.
With the food processor running, gradually add the olive oil in a steady stream. Continue processing until the mixture becomes a smooth pesto consistency.
Season the pesto with salt and pepper to taste. Add the lemon juice and pulse again to combine.
Transfer the rapini pesto to a bowl or jar. Use it immediately as a sauce for pasta, a spread on bread, or a flavorful topping for various dishes.