Cook the noodles in a large saucepan of lightly salted boiling water for 5–6 minutes, or according to packet instructions, until al dente. Drain and return to the pan to keep warm.
Meanwhile, remove the tough outer leaves from the lemon grass and roughly chop the core. Place in a food processor with all the remaining ingredients, except the oil and fish sauce, and blend to a smooth paste, scraping down the sides of the bowl with a spatula from time to time. With the processor still running, add the oil and fish sauce.
Stir the pesto into the warm noodles, divide between 4 bowls and serve immediately with lime wedges.