You can make sauces ahead of time. Salt both sides of the lamb chops. Heat oil in a large nonstick skillet over high heat. Cook in two batches, turning once until chops are deep brown and cooked to medium-rare, 9 to 11 minutes total. Serve with sauces.
For the red sauce: Combine the water, sundried tomatoes, basil, vinegar, sugar, cumin, salt, garlic and black pepper in a food processor and process until smooth.
For the green sauce: Combine the parsley, mint, olive oil, almonds, anchovies and lemon juice in a food processor and process until smooth.
Sauces can be made ahead and stored in airtight containers in the fridge up to a day in advance.
*To French lamb chops, cut any excess meat from the end of each rib, scraping bone clean with the back of a knife. You can also ask your butcher to prepare the chops for you in this manner.