Add the lentils, rice, and water to a large pot. Heat over a medium-high flame until it reaches a boil. Then place a lid on the pot and lower the flame and allow the lentils and rice to simmer for 15 minutes. Add the artichoke hearts and cook until the lentils are fork tender and the liquid has been absorbed, approximately 5 minutes. If there is any remaining liquid when the lentils and rice are tender, drain it off.
Add the lentils and rice to a large bowl. Add the tomatoes, olives, onion, and celery. Toss to combine.
Add all of the dressing ingredients to a cruet or lidded jar. Shake to mix. Drizzle the dressing over the salad. Then toss well to coat.
Serve immediately or refrigerate the salad to serve cold. Top with feta cheese if desired.
Notes
Make-Ahead Tip: This salad can be made in advance and stored in the refrigerator for up to 4 days.