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We demonstrate octave-spanning supercontinuum generation in unpoled lithium niobate waveguides, which are engineered to possess anomalous dispersion and pumped by a turn-key femtosecond laser centered at 1560 nm. Tunable dispersive waves and strong phase-matched second-harmonic generation are both observed by controlling the widths of the waveguides. The major features of the experimental spectra are reproduced by numerical modeling of the generalized nonlinear Schrödinger equation, which can be used to guide waveguide designs for tailoring the supercontinuum spectrum. Our results identify a path to a simple and integrable supercontinuum source in lithium niobate nanophotonic platform and will enable new capabilities in precision frequency metrology.