Transient rheological behaviors of lyotropic polymer liquid crystals with polydomain structure have been investigated not only by two different experimental methods but also by Larson-Doi polydomain model. One of the experiments was the phase modulated flow birefringence technique, and the other was mechanical method involving both shear stress and dynamic modulus measurements. In case of either flow reversal or step changes in shear rates, the damped oscillatory responses of shear stress and birefringence were observed with similar periods. The periods were compared with those predicted by Larson-Doi polydomain model, which tells us that the period is only a function of the dimensionless concentration. It was shown that Larson-Doi theory can predict the global pictures fairly well but not the detailed transient behaviors by comparing the experimental result with the model predictions. To examine the quiescent domain structure both the shear stress relaxation modulus and dynamic moduli were measured. The quiescent polydomain structures of the lyotropic system can be easily destroyed by shearing and the critical strain of the destruction can be determined by measuring the stress relaxation after step strain. The most striking result of this study is that structure evolution during flow reversal may include the changes of both domain size and its orientation in an oscillatory manner. It can serve as a basic idea to build a more general kinetic theory on the polydomain lyotropic system.