Combine lemon juice, capers, olives, vinegar, garlic, and enough water to cover the salmon in a large skillet over medium-high heat. Bring to a boil and add salmon. Reduce heat to medium-low. Let simmer, covered, until salmon is opaque and easily flaked with a fork, about 10 minutes.
Remove salmon from the liquid. Let liquid simmer until reduced by half, about 5 minutes. Add tomatoes and basil; cook and stir the sauce until tomatoes begin to break down, about 3 minutes. Spoon sauce over the salmon to serve.