Low-loss photonic waveguides in lithium niobate offer versatile functionality as nonlinear frequency converters, switches, and modulators for integrated optics. Combining the flexibility of laser processing with liquid phase epitaxy we have fabricated and characterized lithium niobate channel waveguides on lithium niobate and lithium tantalate. We used liquid phase epitaxy with K2O flux on laser-machined lithium niobate and lithium tantalate substrates. The laser-driven rapid-prototyping technique can be programmed to give machined features of various sizes, and liquid phase epitaxy produces high quality single-crystal, lithium niobate channels. The surface roughness of the lithium niobate channels on a lithium tantalate substrate was measured to be 90 nm. The lithium niobate channel waveguides exhibit propagation losses of 0.26 ± 0.04 dB/mm at a wavelength of 633 nm. Second harmonic generation at 980 nm was demonstrated using the channel waveguides, indicating that these waveguides retain their nonlinear optical properties.