Whisk together the ketchup, vinegar, agave, brown sugar, Worcestershire, paprika, salt and pepper in a medium bowl. Whisk in the oil in a slow, steady stream until the dressing is emulsified.
Put the lettuce, red onion and cucumber in a large bowl and toss with enough vinaigrette to coat. Serve immediately.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.