In a medium pot, boil water and cook bowtie pasta according to package instructions.
While the pasta is cooking, combine the lemon juice, oil, salt and pepper in a small bowl to make the dressing. Stir and set aside.
Add the frozen peas to a colander. When the pasta is done cooking, drain the pasta over the peas, letting the hot water defrost them. Rinse with cold running water and drain well.
Dump the cooked pasta and peas into a large serving bowl. Add in the arugula and the dressing. Gently toss until everything is mixed and evenly coated in dressing.