First: It was Lace Cornbread... not "lacey".
Second: Two restaurants by the little bridge on the Causeway offered it.... The Oasis and The Reef. Who had it first is debatable. The Oasis is now The Oasis Suites Hotel and The Reef is now the fishing parking lot.
Third: The recipe above is not totally correct. It was never in the form of a patty and it was only cooked on one side. The batter was extremely thin and poured over the entire (peanut oil coated) griddle. As the water evaporated, multiple holes formed creating the lace effect. When golden brown, it was broken up (much like peanut brittle) and served in wax paper lined baskets. It was only about 1/8" thick, very crispy, salty, greasy and soooo delicious!!!
I spent most of my summers from the late 1950's to the early 1970's at the Oasis and certainly ate more than my share of Lace Cornbread.