The study of graph burning is a crucial area in graph theory, providing insight into the spread of influence, information, or fire across networks. This paper investigates the burning number of triangular grid graphs and Sierpinski gasket graphs, which represent a class of lattice-based and fractal architectures. For triangular grids, we derive a lower bound for the burning number and provide a mathematical framework supporting its validity. Similarly, for Sierpinski gasket graphs, we establish new lower bounds by analyzing their recursive structure and boundary-vertex distribution. Our results emphasize the relationship between the graph’s structural properties and the derived lower bounds on their burning numbers. These findings improve the theoretical understanding of burning dynamics in triangular-like architectures, with potential applications in network design and resource allocation.