Toss shrimp with oil, thyme, and garlic on a rimmed baking sheet. Sprinkle with salt and pepper. Bake until the shrimp are pink and firm, 8 to 10 minutes.
Transfer the shrimp to a large bowl (discard thyme and garlic). Add lemon juice and stir to coat. Gently stir in cucumber, tomatoes, and basil. Arrange the shrimp and vegetables in a serving bowl. Serve drizzled with any dressing left in the bowl and garnish with more basil, if desired.