Rinse and pat the meat dry. Place in a sealable plastic bag or small glass dish. In a medium bowl combine 1 tablespoon of the lime juice, soy sauce, canola oil, brown sugar, garlic, ginger and red curry paste. Pour half the mixture into the bag with the meat. Add the remaining 2 tablespoons lime juice to the bag. Seal tightly, and marinate meat in refrigerator at least 4 hours or overnight, turning occasionally. Reserve the rest of the mixture refrigerated, to dress the salad.
Spray grill or grill pan with cooking spray and preheat. Grill steak until medium-rare, about 5 minutes per side, depending on desired doneness. Let rest until room temperature then slice thinly against the grain.
Combine lettuce, sliced shallot, cilantro, basil and beef in a salad bowl, reserving a few shallots for garnish. Add the reserved dressing and toss to coat. Divide salad among 4 plates and garnish with reserved sliced shallots.