Measurements of the storage modulus of suspensions of marble particles in a surfactant-based lyotropic liquid-crystalline medium (lamellar, smectic B) are reported. The suspension is a model system for several food and consumer products. The storage modulus is found to remain nearly constant with an increase in the particle volume fraction until a critical value is reached, beyond which a sharp increase in the storage modulus is obtained. The critical volume fraction is found to increase with an increase in particle size. The storage modulus of the suspensions exhibits a power law dependence on the oscillation frequency, and the power law exponent decreases sharply near the critical volume fraction. The experimental data indicate a transition from a multidomain lamellar liquid-crystalline structure to a structure with a rigid sample spanning network. A network model for the suspension is proposed in which a large number of parallel lamellae bridge randomly placed particles with surfaces closer than a specified distance, the maximum layer size (sm). The network formation is essentially a continuum percolation problem, for which the dimensionless critical number density is found by numerical simulations to be alpha(c) = rho(c)(1/3)L(m) approximate to 0.87 where L-m is the maximum distance between the centers of bonded particles and rho(c) is the critical number density. The modulus (G(c)) of the percolation network is obtained computationally as the stress required for a small tensile deformation of the network. The computed modulus is found to be of the form G(c) proportional to rho(2/3)(alpha - alpha(c))(2.5), which is in good agreement with experimental data.