Bring a large pot of salted water to a boil. Add the squid ink pasta and cook until al dente. Reserve about 1/2 cup of the pasta water, then drain the pasta.
While the pasta cooks, heat the olive oil in a large skillet over medium heat. Add the minced garlic and red pepper flakes, and cook for about 1 minute until fragrant. Pour in the white wine and let it simmer for 2 minutes.
Add the halved cherry tomatoes and season with salt and pepper. Allow the tomatoes to soften, about 3 minutes.
Add the drained pasta, lemon juice, butter, and a few tablespoons of the reserved pasta water to the skillet, tossing well to coat the pasta in the sauce. If desired, add more pasta water until the sauce reaches your desired consistency.
Remove from heat and garnish with chopped basil if desired, then serve immediately.