An experimental study of the O-16(e,e(')K(+))(Lambda)N-16 reaction has been performed at Jefferson Lab. A thin film of falling water was used as a target. This permitted a simultaneous measurement of the p(e,e(')K(+))Lambda,Sigma(0) exclusive reactions and a precise calibration of the energy scale. A ground-state binding energy of 13.76 +/- 0.16 MeV was obtained for N-16(Lambda) with better precision than previous measurements on the mirror hypernucleus O-16(Lambda). Precise energies have been determined for peaks arising from a Lambda in s and p orbits coupled to the p(1/2) and p(3/2) hole states of the N-15 core nucleus.