Thin-film lithium niobate (TFLN) is an emerging platform for compact, low-power nonlinear-optical devices, and has been used extensively for near-infrared frequency conversion. Recent work has extended these devices to mid-infrared wavelengths, where broadly tunable sources may be used for chemical sensing. To this end, we demonstrate efficient and broadband difference frequency generation between a fixed 1-µm pump and a tunable telecom source in uniformly-poled TFLN-on-sapphire by harnessing the dispersion-engineering available in tightly-confining waveguides. We show a simultaneous 1-2 order-of-magnitude improvement in conversion efficiency and ∼5-fold enhancement of operating bandwidth for mid-infrared generation when compared to equal-length conventional lithium niobate waveguides. We also examine the effects of mid-infrared loss from surface-adsorbed water on the performance of these devices.