Preheat oven to 375 degrees F (190 degrees C). Brush 1 tablespoon olive oil over spaghetti squash halves. Place on a baking sheet.
Bake squash in the preheated oven until easily pierced with a knife, about 30 minutes. Remove from oven and cool until easily handled. Scrape insides of squash into spaghetti strands with a fork.
Heat remaining 1 tablespoon olive oil in a large skillet over medium-high heat. Cook spinach until mostly wilted, about 2 minutes. Add garlic; cook for 30 seconds. Add shrimp and tomatoes; cook and stir until shrimp is almost opaque throughout, about 4 minutes. Season with salt and pepper. Add parsley; toss to combine. Pour in chicken broth; cook until heated through, 4 to 5 minutes. Add the spaghetti squash strands; mix in lemon juice and zest.