We have investigated the lateral charge transport in a multilamellar network of crystalline structures of poly(3-hexylthiophene) (P3HT) embedded in a matrix of small crystallites and amorphous polymers resulting from crystallization at temperatures close to the melting point. Removing the matrix by an appropriate washing process allowed us to observe a power-law increase of the maximum current (I-max) passing from the conductive tip across the polymer crystalline structure into the substrate with increasing number (N) of interconnected edge-on lamellae: I-max similar to N-2/3. Varying isothermal crystallization temperature and crystallization time allowed to tune the morphological structure and to increase charge transport through the network of lamellar crystals by up to a factor of twenty. Our results suggest that the efficiency of charge transport can be increased by the cumulative contributions of a large number of interconnected crystalline lamellae, indicating a potential pathway for improving the performance of various organic electronics devices and related applications.