Microwave photonics, a field that crosscuts microwave/millimeter-wave engineering with optoelectronics, has sparked great interest from research and commercial sectors. This multidisciplinary fusion can achieve ultrawide bandwidth and ultrafast speed that were considered impossible in conventional chip-scale microwave/millimeter-wave systems. Conventional microwave-to-photonic converters, based on resonant acousto-optic modulation, produce highly efficient modulation but sacrifice bandwidth and limit their applicability for most real-world microwave signal-processing applications. In this paper, we build highly efficient and wideband microwave-to-photonic modulators using the acousto-optic effect on suspended lithium niobate thin films. A wideband microwave signal is first piezoelectrically transduced using interdigitated electrodes into Lamb acoustic waves, which directly propagates across an optical waveguide and causes refractive index perturbation through the photoelastic effect. This approach is power-efficient, with phase shifts up to $0.0166\mathrm{rad}/\surd \mathrm{mW}$ over a 45 μm modulation length and with a bandwidth up to 140 MHz at a center frequency of 1.9 GHz. Compared to the state-of-the-art, a $9\times$ more efficient modulation has been achieved by optimizing the acoustic and optical modes and their interactions.