Artichoke Arugula Salad

2 C water
1/4 C lemon juice
3 medium artichokes
5 C baby arugula
1 C thin vertically sliced red onion
1/2 C shaved Parmigiano-Reggiano cheese

Combine water and lemon juice in large bowl. Trim about 2" from top of each artichoke.  Cut each in half vertically.  Remove fuzzy thistle from bottom with a spoon.  Trim any remaining leaves and dark green layer from base.  Place halves in lemon water. (or use canned artichoke hearts, well rinsed, then put in lemon water) Combine 2 T oil, 2 T juice, 1/4 t salt & 1/4 t pepper in large bowl, stir with whisk.  Thinly vertically slice artichokes.  Add artichokes, arugula, and onion to bowl.  Toss to coat.  Top with shaved cheese