Combine cream cheese with the lobster base, pepper, garlic, ginger and lemon, stirring well with a fork. Taste and adjust seasoning as desired, lemon zest may also be added. Gently fold in onions and lobster.
Place 6 wontons on a cutting board, brushing the edges with water. Place 1/2 tsp filling into each wonton, pressing out air and sealing edges well to form a triangle. Stack on a plate dusting with cornstarch to avoid sticking, store in refrigerator until time to fry.
Deep fry in hot oil until golden brown, serve immediately.