Prepare a grill for medium-high heat (or heat a grill pan over medium-high heat); preheat 5 minutes. Skewer shrimp and drizzle with oil; season with salt and pepper. Brush with pesto.
Grill, turning occasionally, until shrimp is opaque, 4 to 5 minutes. Transfer to a platter.
Grill lemons cut side down until charred in spots, 2 to 3 minutes. Arrange next to shrimp for squeezing over. Serve with more pesto alongside.
