Parametric partial differential equations (PDEs) are fundamental to many problems in science and engineering. These problems require repeatedly solving the same governing PDE across parameter ranges. Classical numerical solvers require recomputation for each parameter instance, leading to prohibitive costs. Existing neural network-based approaches only partially resolve this limitation. Physics-informed neural networks often require retraining when parameters change, while operator learning methods depend on large simulation datasets that are expensive to generate. Learning a simulation data-free framework that governs entire parametric PDE families, only through the PDE, initial and boundary conditions, via a single model remains an open challenge. This work introduces a lifelong physics-informed learning framework for parametric PDEs. The method builds a latent representation of the parametric space and poses parameter variations as a unified learning problem rather than independent tasks. Spatial–temporal coordinates and PDE parameters are encoded separately and fused in a shared latent space. This design captures cross-parameter structure while preserving physical constraints. The model is trained using PDE residuals, initial conditions, and boundary conditions, and no labeled numerical solutions are required. The trained model is further adapted to unseen, out-of-domain parameters using a low-rank fine-tuning strategy. Instead of retraining the whole network, only a small set of latent weights is updated. This fine-tuning enables continuous adaptation at low computational cost and supports a lifelong learning paradigm. The method aims to maintain the accuracy within the training domain and facilitate stable generalization. Numerical experiments on benchmark parametric PDEs demonstrate reduced error and lower adaptation cost compared to standard physics-informed neural network variants. The work addresses existing challenges in parametric neural PDE solving: data dependence, weak cross-parameter generalization, and expensive retraining. Broader impact spans engineering applications where repeated PDE solves dominate runtime, including optimization and uncertainty-aware design.