Crab with Romaine, Dill Sauce, and Sunflower Seeds

Place sunflower seeds in jar and pour in cold water to cover. Seal jar and let seeds sit at least 8 hours and up to 12 hours.
Drain sunflower seeds and return to jar. Cover with a double layer of cheesecloth, secure with a rubber band, and let seeds sit until just beginning to sprout, at least 12 hours and up to 1 day. Pat dry with paper towels.
Heat vegetable oil in a medium saucepan fitted with thermometer over medium-high until thermometer registers 350°F. Carefully add sunflower seeds and cook, swirling pan, until puffed and golden brown, about 3 minutes. Using a slotted spoon, transfer to paper towels to drain; season with salt. Let cool.
Cook chopped dill in a large saucepan of boiling salted water just until wilted and bright green, about 30 seconds. Immediately transfer to a bowl of ice water and swish around to cool as quickly as possible. Drain dill and gently squeeze to remove excess water.
Blend dill, buttermilk, and milk in a blender until mixture is bright green and smooth. With motor running, gradually stream in 1/4 cup sunflower oil followed by guar gum, if using (guar gum will give the sauce body without impacting flavor; if omitting, sauce will be a bit runny but equally tasty); season with salt. Transfer dill sauce to a medium bowl. Cover and chill.
Prepare a grill for medium-high heat. Lightly drizzle cut sides of romaine with more sunflower oil; season with salt. Grill, cut side down, until grill marks appear but lettuce is still very crunchy, about 45 seconds. (Or char in a grill pan over medium-high.) Transfer to a platter; let cool.
Heat crabmeat, olive oil, lemon zest, and lemon juice in a medium saucepan over low, stirring gently, until slightly warm; season with salt.
Divide crab mixture among plates. Gently dip romaine in dill sauce and turn to coat completely, letting excess drip back into bowl. Arrange over crab; top with dill sprigs and fried sunflower seeds.
Dill sauce can be made 1 day ahead. Keep chilled.