Add white vinegar to a pot of well-salted water and bring to a boil. Turn off heat and place lobster in the water for 4 minutes. Transfer lobster to a bowl of ice water to cool. Remove whole tail meat and reserve.
Heat oil in a sauté pan over medium-high heat. Add onion and cook 1–2 minutes until it starts to soften. Add chard and cook until chard and onion are tender, about 3 minutes longer. Season with salt to taste and keep warm over low heat.
Boil wine, rice vinegar, shallot and ¼ teaspoon kosher or sea salt in a saucepan until reduced by about half.
While liquid is reducing, preheat outdoor grill or stovetop grill pan. Melt 4 tablespoons butter over low heat and keep warm.
Remove reduced sauce from heat and whisk in 8 tablespoons butter, cut into small cubes, piece by piece until fully melted and incorporated into a smooth sauce (return the pan to low heat if necessary to melt butter). Whisk in the grapefruit pieces and cover with foil to keep sauce warm.
Brush lobster tails with melted butter, and season with salt. Grill over high heat, turning once, until lightly charred and heated through, about 2 minutes total. Serve lobster over chard, with grapefruit sauce spooned on top as desired. Serves 4.