Put the lentils and bay leaf in a saucepan and cover with water by about 2 inches. Bring to a boil, then lower to a gentle simmer.
Cook uncovered for 18–25 minutes, until the lentils are tender but still hold their shape. Start tasting at 15 minutes. Add 1/2 teaspoon salt in the last 5 minutes.
Drain well, discard the bay leaf, and spread the lentils on a tray to cool for 10 minutes.
Meanwhile whisk the olive oil, lemon juice, oregano, garlic, mustard, 1/4 teaspoon salt and plenty of pepper in a large bowl.
Add the warm lentils to the dressing and toss; warm lentils absorb flavor better. Let them sit 5 minutes.
Fold in the tomatoes, cucumber, onion, olives and parsley. Taste and adjust the salt and lemon. Scatter the feta over the top.
Serve over the arugula or spinach.