Combine the cherries, sugar, and lemon juice in a medium pot. Stir to combine, and let sit for 15 minutes.
Place the pot over medium-low heat. Cook until the cherries start to soften, and the juices get thick and jammy, 10 to 15 minutes. Transfer to a bowl or container, and let cool completely (may be prepared a day or two in advance).
Be sure to freeze the bowl of your ice cream maker one day in advance before proceeding to the next step.
When ready to make the gelato, combine half of the plain base and half of the cherry jam in the bowl of a food processor. Pulse until well mixed. Whisk the puree into the remaining plain base.
Pour into the freezer bowl of your ice cream maker. Churn for 20 minutes.
Add the remaining cherry jam. Slowly drizzle in the melted chocolate. Churn for 5 minutes more. Transfer the ice cream to a container, cover, and freeze for at least 2 hours before serving.