Measurement of lactate diffusion properties using diffusion-weighted magnetic resonance spectroscopy in vivo may allow elucidating brain lactate cellular compartmentation, which would be of great importance for neuroscience. However, measuring lactate signal is complicated by low signal-to-noise ratio due to low lactate concentration and J-modulation of its 1.3 ppm peak. In this work, we assess the benefits of using a diffusion-weighting spin echo block and spectrally selective refocusing pulses to suppress the effect of J-coupling on the 1.3 ppm lactate resonance, by not refocusing its coupling partner at 4.1 ppm. Two different kinds of spectrally selective pulses, either polychromatic or single-band, are evaluated in the mouse brain at 11.7 T. Almost complete suppression of J-modulation is shown, resulting in an approximately twofold signal increase as compared to a reference STE-LASER sequence (for the specific diffusion times used in this work). Repeated measurements confirm that lactate diffusion-weighted signal attenuation is measured with an approximately twofold precision.