Set grill to medium- heat. Brush corn with oil and salt.
Put on your grill and cook, turning occasionally. Keep cooking until you can see some charring and the kernels are slightly softened. It should take 12 to 15 minutes depending on your grill temperature.
Scrape the corn kernels. Pulse corn kernels and oil in a food processor until smooth.
Add salt, chiles, and lime zest and juice and pulse until combined. Transfer puree to a bowl. Stir in cheese.
Emulsify puree by adding half of the melted butter. Stir well, add more until sauce is creamy and rich.
In cooking the lobster tails, sprinkle paprika evenly over lobster tail meat. Flip tails over and sprinkle remaining butter evenly over meat. To keep tails together, use toothpicks to keep lobster tails sealed.
Add grilled corn puree to cover the meat (you can add it hot or cold). Garnish with chopped chives.
Serving Suggestions: Divide corn kernels puree and sprinkle with chives and more cheese among the plates.