Annually 8500 neonatal deaths are reported in the US due to respiratory failure. Recently, Lung Ultrasound (LUS), due to its radiation free nature, portability, and being cheaper is gaining wide acceptability as a diagnostic tool for lung conditions. However, lack of highly trained medical professionals has limited its use especially in remote areas. To address this, an automated screening system that captures characteristics of the LUS patterns can be of significant assistance to clinicians who are not experts in lung ultrasound (LUS) images. In this paper, we propose a feature extraction method designed to quantify the spatially-localized line patterns and texture patterns found in LUS images. Using the dual-tree complex wavelet transform (DTCWT) and four types of common image features we propose a method to classify the LUS images into 6 common neonatal lung conditions. These conditions are normal lung, pneumothorax (PTX), transient tachypnea of the newborn (TTN), respiratory distress syndrome (RDS), chronic lung disease (CLD) and consolidation (CON) that could be pneumonia or atelectasis. The proposed method using DTCWT decomposition extracted global statistical, grey-level co-occurrence matrix (GLCM), grey-level run length matrix (GLRLM) and linear binary pattern (LBP) features to be fed to a linear discriminative analysis (LDA) based classifier. Using 15 best DTCWT features along with 3 clinical features the proposed approach achieved a per-image classification accuracy of 92.78% with a balanced dataset containing 720 images from 24 patients and 74.39% with the larger unbalanced dataset containing 1550 images from 42 patients. Likewise, the proposed method achieved a maximum per-subject classification accuracy of 81.53% with 43 DTCWT features and 3 clinical features using the balanced dataset and 64.97% with 13 DTCWT features and 3 clinical features using the unbalanced dataset.