Lyotropic liquid crystals (LLCs) are obtained from the self-assembly of amphiphilic block copolymers in the presence of solvents. The LLCs can be used as templates for synthesis of nanoporous polymers. This work describes the kinetics of thermal polymerization in nanoconfined domains of LLC templates by using chemorheological studies at different temperatures. We investigate lamellar and reverse hexagonal LLC phases with the same concentration of monomeric phase. Results show that the polymerization rate decreases in the nanoconfined structure compared to the bulk state due to the segregation effect that increases the local monomer concentration and enhances the termination rate. Additionally, the polymerization rate is faster in the studied reverse hexagonal systems compared to the lamellar ones due to their lower degree of confinement. A higher degree of confinement also induces a lower monomer conversion.