Recent advancements in early assessment of pulmonary hypertension (PH) primarily focus on applying machine learning methods to centralized diagnostic modalities, such as 12-lead electrocardiogram (12L-ECG). Despite their potential, these approaches fall short in decentralized clinical settings, e.g., point-of-care and general practice, where handheld 6-lead ECG (6L-ECG) can offer an alternative but is limited by the scarcity of labeled data for developing reliable models. To address this, we propose a lead-specific electrocardiogram multimodal variational autoencoder (\textsc{LS-EMVAE}), which incorporates a hierarchical modality expert (HiME) fusion mechanism and a latent representation alignment loss. HiME combines mixture-of-experts and product-of-experts to enable flexible, adaptive latent fusion, while the alignment loss improves coherence among lead-specific and shared representations. To alleviate data scarcity and enhance representation learning, we adopt a transfer learning strategy: the model is first pre-trained on a large unlabeled 12L-ECG dataset and then fine-tuned on smaller task-specific labeled 6L-ECG datasets. We validate \textsc{LS-EMVAE} across two retrospective cohorts in a 6L-ECG setting: 892 subjects from the ASPIRE registry for (1) PH detection and (2) phenotyping pre-/post-capillary PH, and 16,416 subjects from UK Biobank for (3) predicting elevated pulmonary atrial wedge pressure, where it consistently outperforms unimodal and multimodal baseline methods and demonstrates strong generalizability and interpretability. The code is available at https://github.com/Shef-AIRE/LS-EMVAE.