The change in the electric potential due to lightning is evaluated. The potential along the lightning channel is a constant which is the projection of the pre-flash potential along a piecewise harmonic eigenfunction which is constant along the lightning channel. The change in the potential outside the lightning channel is a harmonic function whose boundary conditions are expressed in terms of the pre-flash potential and the post-flash potential along the lightning channel. The expression for the lightning induced electric potential change is derived both for the continuous equations, and for a spatially discretized formulation of the continuous equations. The results for the continuous equations are based on the properties of the eigenvalues and eigenfunctions of the following generalized eigenproblem: Find $u \in H_0^1 (\Omega)$, $u \ne 0$, and $\lambda \in \mathbb{R}$ such that $ \langle \nabla u, \nabla v \rangle_{\mathcal{L}} = \lambda \langle \nabla u, \nabla v \rangle_{\Omega} $ for all $v \in H_0^1 (\Omega)$, where $\Omega \subset \mathbb{R}^n$ is a bounded domain (a box containing the thunderstorm), $\mathcal{L}$ is a subdomain (the lightning channel), and $\langle \cdot, \cdot \rangle_{\Omega}$ is the inner product $ \langle \nabla u,\nabla v\rangle_\Omega =\int_{\Omega} \nabla u\cdot\nabla v \; {{\rm d}x}. $