We calculate the bending modulus K of microphase-separated di- and triblock copolymer lamellae in the strong segregation limit. We restrict our attention to triblock architectures of the form A-B-A where the two A-blocks have equal size and chemistry. Inside a triblock lamella some of the chains form "bridges" between two A-regions and some form "loops" into the same A-region. The bending modulus K is found to depend on the chain architecture, as well as the bridging fraction, while the compressional modulus does not. We present results for K as a function off, the total length fraction of A-block. For f = 1/2 bridging triblocks are found to have a bending modulus 13/4 times larger than either (i) those forming loops or (ii) diblocks of half the length. If initially half the triblocks bridge and half loop (at the level of the simplest treatment they have the same energies in a flat layer), the initial ratio of the modulus of a triblock layer to a diblock one is 17/8. However, after deformation, the modulus (and stress) drops as equilibration of bridges to loops occurs. Since the stress is a function of the bridging fraction, we argue that it may provide a probe of the dynamics of the bridge-to-loop process.