Rich phase structures and evolutions of the blends of smectic-nernatic (S-N) liquid crystalline (LC) diblock copolymers and a nematic solvent (5CB) are investigated in a concentrated regime. These types of fully LC systems are macroscopically homogeneous with ordered phase-separated structures on the nanometer scale. By varying the temperature as well as the content of 5CB, the phase diagram of the blends is constructed, where the order-to-order transition (OOT) between lamellar and cylindrical nanostructures can be induced either lyotropically or thermotropically. The temperature and concentration dual-responsive properties are found to be closely related to the selectivity and distribution of 5CB, in addition to its phase transformation at the nematic-isotropic transition. As inferred from the miscibility and phase behaviors of its blends with the respective smectic and nematic homopolyrners, the partition of 5CB in the S-N diblock copolymers and its influence on the phase structures reveal the important role of the LC interactions on the self-assembly of the diblock copolymers.