With motor running, drop garlic into a food processor and finely chop. Stop processor and add onion, jalapeño (to taste), lemon juice, and 1/4 teaspoon salt, then pulse until finely chopped. Let stand at room temperature 30 minutes for flavors to develop. Peel xuxu if skin is tough. Cut xuxu off pit in slices, then cut into 1/4-inch-thick matchsticks. Toss shrimp with 1 teaspoon salt. Heat 3 tablespoons oil in a 12-inch heavy skillet over medium-high heat until it shimmers. Sauté shrimp until just cooked through, 3 to 5 minutes. Transfer to a plate. Sauté xuxu in remaining tablespoon oil in skillet until crisp-tender, about 3 minutes. Return shrimp to skillet, then add hearts of palm and sauté until just heated through. Remove from heat and stir in chile-lemon sauce and cilantro.