We consider the uniqueness of stationary solutions to the Navier-Stokes equation in 3-dimensional exterior domains within the class u ∈ L_{3, ∞} with ∇u ∈ L_{3/2, ∞}, where L_{3, ∞} and L_{3/2, ∞} are the Lorentz spaces. It is shown that if solutions u and v satisfy the conditions that u is small in L_{3, ∞} and v ∈ L₃ + L_∞, then u = v. The proof relies upon the regularity theory for the perturbed Stokes equation.