Cook the spaghetti according to package instructions.
Meanwhile, in a pan set over medium-low heat, sweat out the garlic and onion in butter for 3-4 minutes (do not let them brown).
Add the lime juice and reduce by half. Add the flour and stir. Add the cream and cook for 5 minutes. Add the milk, stir, and turn off the heat.
Once the pasta is cooked, add 80 ml of the cooking water to the sauce, increase the heat to medium-high and add the pasta and chicken. Stir for 3 minutes. Add the fresh cilantro and lime slices, stir, and serve.