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Set up a two-zone fire in your gas or charcoal grill, creating a hotter side and a cooler side for grilling the pizzas.
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Bring a large pot of water to a boil. Boil the lobster for 3 minutes and then submerge in an ice bath. The lobster will not be cooked through yet.
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Once the lobster is cold, remove it from the water and place it on a cutting board with a juice groove.
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Cut the lobster in half lengthwise. Remove the light green tomalley and discard, but if the dark green/black roe sac is present, keep it intact.
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Brush the cut side of the lobster with the grapeseed oil and season with salt and pepper.
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Grill the lobster cut side down on the hot side of the grill, until the meat has nice grill marks and is opaque, 6 to 7 minutes. Allow the grilled lobster to rest for about 5 minutes.
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Remove the meat from the tail and cut into bite-size pieces. Set aside.
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To remove the meat from the claws, use the spine of your knife to crack the shell. Remove the shell, revealing the claw meat. Cut into bite-size pieces and set aside.
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To grill the corn, brush the ears with grapeseed oil and season with salt and pepper to taste.
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Grill on all sides until slightly charred and tender. Allow to cool before removing the kernels.
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To shape the pizza dough, punch down the dough to gently deflate. Stretch the dough into an 1/8-inch-thick round, and lay it on a pizza peel dusted with cornmeal. Brush the top of the dough with garlic grapeseed oil.
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Slide the dough off the peel onto the hotter side of the grill to get a bit of color and crispness. When the dough is firm and slightly crispy, turn it over to toast the other side for a minute.
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Next, slide the crust to the cooler side of the grill and top with the grilled lobster meat and corn. Continue to grill, with the lid closed, until the toppings are hot.
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While the pizza is grilling mix together the crème fraîche and tarragon.
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Remove the pizza from the grill and drizzle with the tarragon crème fraîche.
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Cut into slices and serve.
