The one-boson Lee model of a solvable field theory with nontrivial charge and mass renormalization provides an elementary example of the Lehmann-Symanzik-Zimmermann formalism. The basic quantities of interest in this method of calculation are the vacuum expectation values of time-ordered Heisenberg operators and by studying the analytic properties of the Fourier transforms of these functions, the first nontrivial subspace of the model is solved without resorting to eigenvalue equations. The full Lee model was recently analyzed with this technique and it seems pedagogically appropriate to carry out an analogous calculation in an even more elementary context.