Acute lymphocytic leukemia (ALL) is a rapidly progressing blood cancer that affects the lymphocytes. The diagnosis of ALL typically entails the examination of blood smears under a microscope, processes that are both time-consuming and susceptible to errors. Deep learning (DL) approaches have shown significant promise in automating the classification of ALL from microscopic images. However, the lack of transparency in these models hinders their widespread adoption in clinical settings. This study addresses this challenge by employing fine-tuned EfficientNetV2B3, a DL model, in conjunction with local interpretable model-agnostic explanations (LIME), a technique for explainable artificial intelligence (XAI) technique, to classify microscopic images of ALL. The C-NMC 2019 dataset, which has been augmented to ensure class balance, was utilized for training and evaluation. The proposed approach achieved impressive results, with an average recall, F1-score, and accuracy of 0.9795 and precision of 0.9796. The use of LIME effectively highlights relevant areas for prediction, accurately corresponding to the cell characteristics. The integration of DL and XAI techniques enhances the interpretability of ALL classification models, potentially increasing their trustworthiness and adoption in clinical practice. This study aims to further the development of diagnostic tools that are both precise and transparent for ALL.