We report the discovery of X-ray emission at the position of the old classical nova DK Lacertae using the Swift satellite. Three observations were conducted using the X-Ray Telescope 62 years after the discovery of the nova, yielding 46 source signals in an exposure time of 4.8 ks. A background-subtracted count rate was 9 +/- 2 x 10(-3) counts s(-1), corresponding to a detection significance level of 5 sigma. The X-ray spectrum was characterized by a continuum extending up to about 7 keV, which can be modeled by a power-law component with a photon index of 1.4-5.6, or by a thermal bremsstrahlung component with a temperature of 0.7-13.3 keV, convolved with interstellar absorption with an equivalent hydrogen column density of 0.3-2.4 x 10(22) cm(-2). Assuming a distance of 3900 pc to the source, the luminosity was 10(32)-10(34) erg s(-1) in the 0.3-10 keV energy band. The origin of X-rays is considered to be either mass accretion on the white dwarf or adiabatic shocks in nova ejecta, with the former appearing much more likely. In either case, DK Lacertae represents a rare addition to the exclusive club of X-ray emitting old novae.