Plunge a sharp knife into top of lobster's head just behind its eyes (to kill it quickly); chop into 8–10 pieces.
Heat oil in a large skillet over medium-high heat. Add lobster and any juices and garlic; cook, stirring and turning the lobster pieces, for 1 minute. Add wine and cook until alcohol has evaporated, about 3 minutes. Add tomatoes and cook, stirring occasionally and breaking tomatoes down with the back of a wooden spoon, until sauce gets smoother and thickens slightly, about 10 minutes. Season to taste with salt.
Meanwhile, cook spaghetti in a large pot of boiling salted water over high heat until just tender, 11–13 minutes. Drain, add pasta to sauce, stirring well, and cook a few minutes more. Serve garnished with parsley.