Mince garlic and mash to a paste with a pinch of salt using a large heavy knife.
Core and coarsely chop two thirds of tomatoes. Halve remaining tomatoes crosswise, then rub cut sides of tomatoes against large holes of a box grater set in a large bowl, reserving pulp and discarding skin. Toss pulp with chopped tomatoes, garlic paste, lemon juice, salt, sugar (if using), and pepper.
Let stand until ready to use, at least 10 minutes.
While tomatoes stand, cook pasta in a 6- to 8-quart pot of boiling salted water, uncovered, until al dente, about 2 minutes.
Drain in a colander and immediately add to tomato mixture, tossing to combine.
Sprinkle with basil.
Tomato mixture can stand at room temperature up to 2 hours.
