Lattice Tension Theory (LTT) is a theoretical framework that explores the possibility that observable space is composed of discrete quantum-scale cells whose structural response gives rise to gravitational phenomena. Matter is modeled as persistent configurations of quantum energy packets occupying this cellular network, while occupation modifies the elastic state of the surrounding structure.A central feature of LTT is the distinction between an empty cell, an occupied cell, and a missing or non-operative cell. Under sufficiently strong and sustained loading, the cellular structure may undergo fracture and lose its ability to support ordinary three-dimensional propagation. Such a persistent cell-free region is proposed as a spatial rupture, with black holes interpreted as spatial ruptures surrounded by an active, gravitating boundary.The paper develops both discrete and continuum descriptions of the framework. A variational scalar action leads to a nonlinear gravitational field equation with a load-dependent elastic coefficient, while a corresponding discrete lattice energy provides a microscopic counterpart. The formulation reproduces the Newtonian weak-field limit and admits an exact spherical exterior solution. A surface-source formulation demonstrates how an attractive exterior gravitational field can arise around an excised region without requiring an ordinary matter source in its interior.The study also introduces candidate mechanisms for lattice fracture and repair, higher-dimensional energy exchange, boundary radiation, area-scaling entropy, and a universal ordering parameter distinct from physical clock readings.This work is intended as a foundational formulation rather than a completed alternative to general relativity. Its purpose is to define the physical assumptions and mathematical structure of LTT clearly enough for subsequent numerical simulations, compact-object studies, galaxy-scale tests, propagation analyses, and comparison with observational constraints.