Monitoring aquatic species, especially elusive ones like lobsters, presents challenges. This study focuses on Homarus gammarus (European lobster), a key species for fisheries and aquaculture, and leverages non-invasive Passive Acoustic Monitoring (PAM). Understanding lobster habitats, welfare, reproduction, sex, and age is crucial for management and conservation. While bioacoustic emissions have classified various aquatic species using Artificial Intelligence (AI) models, this research specifically uses H. gammarus bioacoustics (buzzing/carapace vibrations) to classify lobsters by age (juvenile/adult) and sex (male/female). The dataset was collected at Johnshaven, Scotland, using hydrophones in concrete tanks. We explored the efficacy of Deep Learning (DL) models (1D-CNN, 1D-DCNN) and six Machine Learning (ML) models (SVM, k-NN, Naive Bayes, Random Forest, XGBoost, MLP). Mel-frequency cepstral coefficients (MFCCs) were used as features. For age classification (adult vs. juvenile), most models achieved over 97% accuracy (Naive Bayes: 91.31%). For sex classification, all models except Naive Bayes surpassed 93.23%. These strong results demonstrate the potential of supervised ML and DL to extract age- and sex-related features from lobster sounds. This research offers a promising non-invasive PAM approach for lobster conservation, detection, and management in aquaculture and fisheries, enabling real-world edge computing applications for underwater species.