This paper presents a physically based theory to model the strength and lifetime distributions of quasibrittle structures. The theory is derived from the fracture mechanics of atomic lattice cracks propagating through the lattice by tiny jumps over numerous activation energy barriers on the surface of the free energy potential of the lattice, caused by crack length jumps by one atomic spacing. The theory indicates that the strength threshold is zero, and that the strength distribution for a quasibrittle structure depends on its size, as well as geometry, varying from Gaussian distribution (modified by far-left power law tail) for small-size structures, to Weibull distribution for large-size structures. The theory is further extended to model the lifetime distribution of quasibrittle structures under constant loads (creep rupture). It is shown that, for quasibrittle materials, there exists a marked size effect on not only the structural strength but also the lifetime, and that the latter is stronger. For various quasibrittle materials, such as industrial ceramics and fibrous composites, it is demonstrated that the proposed theory correctly predicts the experimentally observed deviations of strength and lifetime histograms from the classical Weibull theory, as well as the deviations of the mean size effect curves from a power law.