This work demonstrates the first implementation of lithium niobate-on-silicon (LNoSi) non-reciprocal acoustic delay lines (ADL) with tunable insertion loss (IL) utilizing the acoustoelectric (AE) effect. Due to the AE effect, the direction- and the intensity-dependent momentum exchange between the drifting electrons in the Si layer and the acoustic phonons can be utilized to break the intrinsic reciprocity of the ADLs in order to control their frequency response. A 5.2 dB improvement in the IL and a 14.2 dB increase in the reverse isolation (i.e. a 19.4 dB non-reciprocal transmission ratio) is achieved through injecting a 400 µA current in one of the ADLs presented here. This opens up possibilities of merging long delays, tunable attenuators, and switches in a single miniaturized device which is a critical stepping stone in fulfillment of full-duplexed microwave systems.