If using fresh snap peas, blanch them in boiling water until tender, 6 to 7 minutes. Drain and cool.
Put peas, basil, garlic, parmesan, pine nuts, salt, and lemon juice in a food processor and process until combined but still chunky.
With the processor still running, slowly pour in the oil through the feed tube. Process the pesto to your desired consistency, add more oil if necessary. Adjust salt.