1. Core, peel, and seed the tomatoes; cut the flesh into 1-inch chunks. Seed the melon, and remove the flesh from the rind; cut into chunks. Place a tablespoon of olive oil in each of two 10- or 12-inch skillets and turn the heat under both to high (you can do this sequentially if you prefer). Add the melon to one and the tomatoes to the other and cook, stirring, until the become juicy, no longer than 2 minutes.
2. Blend together the melon, tomato, water, and basil, along with some salt and pepper. Chill, then add lemon juice to taste and adjust seasoning.