The flow-induced structures of three types of lyotropic liquid crystals with different degrees of flexibility are investigated during simple shear flow. Both optical microscopy and small angle light scattering are used. Different types of structure appear systematically in shear rate regions that can be associated with specific regions of the rheological curves. Changing concentration and temperature does not affect the correlation between rheological and textural transitions. Stress and texture have also been observed in transient experiments when starting from a monodomain. The types of texture that occur at different shear rates under steady state conditions can also be observed as transient structures at a single shear rate.