Research on detecting Tuberculosis (TB) findings on chest radiographs (or Chest X-rays: CXR) using convolutional neural networks (CNNs) has demonstrated superior performance due to the emergence of publicly available, large-scale datasets with expert annotations and availability of scalable computational resources. However, these studies use only the frontal CXR projections, i.e., the posterior-anterior (PA), and the anterior-posterior (AP) views for analysis and decision-making. Lateral CXRs which are heretofore not studied help detect clinically suspected pulmonary TB, particularly in children. Further, Vision Transformers (ViTs) with built-in self-attention mechanisms have recently emerged as a viable alternative to the traditional CNNs. Although ViTs demonstrated notable performance in several medical image analysis tasks, potential limitations exist in terms of performance and computational efficiency, between the CNN and ViT models, necessitating a comprehensive analysis to select appropriate models for the problem under study. This study aims to detect TB-consistent findings in lateral CXRs by constructing an ensemble of the CNN and ViT models. Several models are trained on lateral CXR data extracted from two large public collections to transfer modality-specific knowledge and fine-tune them for detecting findings consistent with TB. We observed that the weighted averaging ensemble of the predictions of CNN and ViT models using the optimal weights computed with the Sequential Least-Squares Quadratic Programming method delivered significantly superior performance (MCC: 0.8136, 95% confidence intervals (CI): 0.7394, 0.8878, p < 0.05) compared to the individual models and other ensembles. We also interpreted the decisions of CNN and ViT models using class-selective relevance maps and attention maps, respectively, and combined them to highlight the discriminative image regions contributing to the final output. We observed that (i) the model accuracy is not related to disease region of interest (ROI) localization and (ii) the bitwise-AND of the heatmaps of the top-2-performing models delivered significantly superior ROI localization performance in terms of mean average precision [mAP@(0.1 0.6) = 0.1820, 95% CI: 0.0771,0.2869, p < 0.05], compared to other individual models and ensembles. The code is available at https://github.com/sivaramakrishnan-rajaraman/Ensemble-of-CNN-and-ViT-for-TB-detection-in-lateral-CXR.