An experimental study of the (16)O(e,e'K(+))(Lambda)(16)N 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 (Lambda)(16)N with better precision than previous measurements on the mirror hypernucleus (Lambda)(16)O. 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 (15)N core nucleus.