  In this paper, we introduce and analyze a lowest-order locking-free weak
Galerkin (WG) finite element scheme for the grad-div formulation of linear
elasticity problems. The scheme uses linear functions in the interior of mesh
elements and constants on edges (2D) or faces (3D), respectively, to
approximate the displacement. An $H(div)$-conforming displacement
reconstruction operator is employed to modify test functions in the right-hand
side of the discrete form, in order to eliminate the dependence of the
$Lam\acute{e}$ parameter $\lambda$ in error estimates, i.e., making the scheme
locking-free. The method works without requiring $\lambda \|\nabla\cdot
\mathbf{u}\|_1$ to be bounded. We prove optimal error estimates, independent of
$\lambda$, in both the $H^1$-norm and the $L^2$-norm. Numerical experiments
validate that the method is effective and locking-free.
