Respiratory diseases are among the leading causes of death, with many individuals in a population frequently affected by various types of pulmonary disorders. Early diagnosis and patient monitoring (traditionally involving lung auscultation) are essential for the effective management of respiratory diseases. However, the interpretation of lung sounds is a subjective and labor-intensive process that demands considerable medical expertise, and there is a good chance of misclassification. To address this problem, we propose a hybrid deep learning technique that incorporates signal processing techniques. Parallel transformation is applied to adventitious respiratory sounds, transforming lung sound signals into two distinct time-frequency scalograms: the continuous wavelet transform and the mel spectrogram. Furthermore, parallel convolutional autoencoders are employed to extract features from scalograms, and the resulting latent space features are fused into a hybrid feature pool. Finally, leveraging a long short-term memory model, a feature from the latent space is used as input for classifying various types of respiratory diseases. Our work is evaluated using the ICBHI-2017 lung sound dataset. The experimental findings indicate that our proposed method achieves promising predictive performance, with average values for accuracy, sensitivity, specificity, and F1-score of 94.16%, 89.56%, 99.10%, and 89.56%, respectively, for eight-class respiratory diseases; 79.61%, 78.55%, 92.49%, and 78.67%, respectively, for four-class diseases; and 85.61%, 83.44%, 83.44%, and 84.21%, respectively, for binary-class (normal vs. abnormal) lung sounds.