Fire up your grill for direct and indirect cooking. You'll use the direct heat to sear the cedar plank. You'll use indirect (low or no flame under the blank) heat to cook the shrimp.
Pat the shrimp dry.
Toss the shrimp with half of the pesto.
Toss shrimp in mixture, coating it all over.
Place your cedar plank over the direct heat for 15 or so minutes until charred on one side.
Move the plank to indirect heat. Add the shrimp. Drizzle lightly with oil. Note: You may not need much if any oil, depending on how thick your pesto is. A lighter thinner pesto may not require any. You only need the oil to slightly 'loosen' or thin the pesto.
Place the lemons over direct heat.
Close the grill lid and let cook until the shrimp start to turn pink.
Spoon the remaining pesto over the shrimp. Continue cooking until the shrimp are done. The lemons should get a nice char on them.
Drizzle two halves of the lemons over the shrimp (I used grill tongs to squeeze them).
Serve shrimp on the plank with the remaining lemon halves for juicing.