Sauce:

Place wine, onion, green onion, thyme, and lime juice in a small saucepan. Boil until mixture is reduced to ? cup, about 5 minutes. Strain; discard solids. Return wine mixture to saucepan. Add cream; boil until reduced to ? cup, about 5 minutes. Remove from heat; add butter a few cubes at a time, stirring between additions until melted and smooth. Season with salt and pepper.

Lobster:

Prepare barbecue (medium-high heat). Mix lime juice, oil, and chile in small bowl for marinade. Place lobster tail, flesh side up, in 13x9x2-inch baking dish. Drizzle with marinade; let stand 15 minutes. Sprinkle lobster tails with paprika; sprinkly lightly with salt. Grill lobster tails until cooked through, brushing frequently with melted butter and turning occasionally, about 8 minutes.

Rewarm sauce over low heat and divide among 4 small ramekins or bowls. Place half of lobster tail and 1 ramekin of sauce on each of 4 plates.