High-harmonic generation (HHG) provides short-wavelength light that is useful for precision spectroscopy and probing ultrafast dynamics. We report efficient, phase-coherent harmonic generation up to the ninth order (333 nm) in chirped periodically poled lithium niobate waveguides driven by phase-stable ≤ 12 n J , 100 fs pulses at 3 µm with 100 MHz repetition rate. A mid-infrared to ultraviolet-visible conversion efficiency as high as 10% is observed, among an overall 23% conversion of the fundamental to all harmonics. We verify the coherence of the harmonic frequency combs despite the complex highly nonlinear process. Accommodating the extreme spectral bandwidth, numerical simulations based on a single broadband envelope equation with only quadratic nonlinearity give estimates for the conversion efficiency within approximately 1 order of magnitude over a wide range of experimental parameters. From this comparison between theory and experiment, we identify a dimensionless parameter capturing the competition between three-wave mixing and group-velocity walk-off of the harmonics that governs the cascaded HHG physics. We also gain insights into spectral optimization via tuning the waveguide poling profile and pump pulse parameters. These results can inform cascaded HHG in a range of different platforms.