I struggled with doing Atkins as a vegetarian as I was determined to include the induction phase.
I found this very easy once I bought the two excellent vegetarian low-carb books by Rose Elliot.
Both are cheap on Amazon and the recipes are so good that my (non-veggie) housemate who was on Atkins started using those in preference to the Atkins recipes because they looked tastier.
Buying those books would be my biggest tip to anyone, particularly if you're wanting to do a 20g carb induction phase as a vegetarian.