Employing diagrammatic techniques, a model for the reactions $^{1}\mathrm{H}(\ensuremath{\gamma},{K}^{+})\ensuremath{\Lambda}$ and $^{1}\mathrm{H}(e,{e}^{\ensuremath{'}}{K}^{+})\ensuremath{\Lambda}$ is derived with the coupling constants being determined phenomenologically by a least-squares fit to the available data. We find a strong sensitivity of the photoproduction process to $t$-channel exchange terms. The inclusion of the kaon resonance $Q1(1280 \mathrm{MeV})$ brings the dominant $K\ensuremath{\Lambda}N$ coupling constant in agreement with predictions from the analysis of $\mathrm{Kp}$ scattering data. An excellent fit to the electroproduction data confirms former measurements of the kaon radius.