The mean alpha-to-iron abundance ratio ([$alpha$/Fe]) of galaxies is sensitive to the chemical evolution processes at early time, and it is an indicator of star formation timescale ($tau_{{rm SF}}$). Although the physical reason remains ambiguous, there is a tight relation between [$alpha$/Fe] and stellar velocity dispersion ($sigma$) among massive early-type galaxies (ETGs). However, no work has shown convincing results as to how this relation behaves at low masses. We assemble 15 data sets from the literature and build a large sample that includes 192 nearby low-mass ($18<sigma<80$~kms) ETGs. We find that the [$alpha$/Fe]-$sigma$ relation generally holds for low-mass ETGs, except in extreme environments. Specifically, in normal galaxy cluster environments, the [$alpha$/Fe]-$sigma$ relation and its intrinsic scatter are, within uncertainties, similar for low-mass and high-mass ETGs. However, in the most massive relaxed galaxy cluster in our sample, the zero point of the relation is higher and the intrinsic scatter is significantly larger. By contrast, in galaxy groups the zero point of the relation offsets in the opposite direction, again with substantial intrinsic scatter. The elevated [$alpha$/Fe] of low-mass ETGs in the densest environments suggests that their star formation was quenched earlier than in high-mass ETGs. For the low-mass ETGs in the lowest density environments, we suggest that their more extended star formation histories suppressed their average [$alpha$/Fe]. The large scatter in [$alpha$/Fe] may reflect stochasticity in the chemical evolution of low-mass galaxies.
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