Bring a large pot of salted water to a boil. Add lima beans and carrots and cook for 4 minutes. Add asparagus and cook 1 minute longer. Using a slotted spoon, remove vegetables and rinse under cold water to stop cooking. Add fettuccine to water and cook until tender, 8 to 10 minutes (or according to package directions). Drain, reserving 1/2 cup cooking water.
When fettuccine has cooked for about 5 minutes, melt butter in a large frying pan over mediumhigh heat. Add garlic and sauté until fragrant, 1 minute. Add vegetables, season with salt and pepper, and sauté until vegetables look glazed and are crisp-tender, 3 to 4 minutes. Add the drained fettuccine and 1/4 cup reserved cooking water and toss well. Transfer to a large, shallow serving bowl and toss with Parmesan and parsley.
Add ricotta to hot pasta by spoonfuls and toss gently to combine. Season with salt and pepper. If pasta appears dry, drizzle in a little more cooking water. Serve immediately.