Large-scale models for learning fixed-dimensional cross-lingual sentence representations like LASER (Artetxe and Schwenk, 2019b) lead to significant improvement in performance on downstream tasks. However, further increases and modifications based on such large-scale models are usually impractical due to memory limitations. In this work, we introduce a lightweight dual-transformer architecture with just 2 layers for generating memory-efficient cross-lingual sentence representations. We explore different training tasks and observe that current cross-lingual training tasks leave a lot to be desired for this shallow architecture. To ameliorate this, we propose a novel cross-lingual language model, which combines the existing single-word masked language model with the newly proposed cross-lingual token-level reconstruction task. We further augment the training task by the introduction of two computationally-lite sentence-level contrastive learning tasks to enhance the alignment of cross-lingual sentence representation space, which compensates for the learning bottleneck of the lightweight transformer for generative tasks. Our comparisons with competing models on cross-lingual sentence retrieval and multilingual document classification confirm the effectiveness of the newly proposed training tasks for a shallow model.