In recent years, a variety of deep learning techniques and methods have been adopted to provide AI solutions to issues within the medical field, with one specific area being audio-based classification of medical datasets. This research aims to create a novel deep learning architecture for this purpose, with a variety of different layer structures implemented for undertaking audio classification. Specifically, bidirectional Long Short-Term Memory (BiLSTM) and Gated Recurrent Units (GRU) networks in conjunction with an attention mechanism, are implemented in this research for chronic and non-chronic lung disease and COVID-19 diagnosis. We employ two audio datasets, i.e. the Respiratory Sound and the Coswara datasets, to evaluate the proposed model architectures pertaining to lung disease classification. The Respiratory Sound Database contains audio data with respect to lung conditions such as Chronic Obstructive Pulmonary Disease (COPD) and asthma, while the Coswara dataset contains coughing audio samples associated with COVID-19. After a comprehensive evaluation and experimentation process, as the most performant architecture, the proposed attention BiLSTM network (A-BiLSTM) achieves accuracy rates of 96.2% and 96.8% for the Respiratory Sound and the Coswara datasets, respectively. Our research indicates that the implementation of the BiLSTM and attention mechanism was effective in improving performance for undertaking audio classification with respect to various lung condition diagnoses.