I did some research on Greek salads recently and found that basically only in the Detroit area do restaurants put sliced beets in them. You can find Greek salads with or without lettuce but always feta cheese, tomatoes, kalamata olives, and onion. So go ahead and put whatever you like in them. Here are some suggestions:
Green or red bell pepper
Here's a quick dressing recipe:
Combine the juice of 1/2 a lemon,1/2 cup olive oil, one clove of crushed garlic, 1/4 tsp dried oregano and salt and pepper into a jar with a lid or the mini food processor.