Most existing contrastive learning-based sequential recommendation (SR) methods rely on random operations (e.g., crop, reorder, and substitute) to generate augmented sequences. These methods often struggle to create positive sample pairs that closely resemble the representations of the raw sequences, potentially disrupting item correlations by deleting key items or introducing noisy iterac, which misguides the contrastive learning process. To address this limitation, we propose Learnable sequence Augmentor for triplet Contrastive Learning in sequential Recommendation (LACLRec). Specifically, the self-supervised learning-based augmenter can automatically delete noisy items from sequences and insert new items that better capture item transition patterns, generating a higher-quality augmented sequence. Subsequently, we randomly generate another augmented sequence and design a ranking-based triplet contrastive loss to differentiate the similarities between the raw sequence, the augmented sequence from augmenter, and the randomly augmented sequence, providing more fine-grained contrastive signals. Extensive experiments on three real-world datasets demonstrate that both the sequence augmenter and the triplet contrast contribute to improving recommendation accuracy. LACLRec significantly outperforms the baseline model CL4SRec, and demonstrates superior performance compared to several state-of-the-art sequential recommendation algorithms.