The more I read up about these types of ships the odder it seems that LCS(L)'s are limited to different TF types then the LCI(X) types. LCS(L) was used in the same capacity as LCI(G, R, and M) types, and was based on the same LCI hull. The LCS was just purpose built from hull up, but still an LCI hull, whereas the LCI (G,R,M) were simply modified LCI's.
Of the different types of landing ships. LST, LSD, LSV, LSM, LCI, LCI(R), LCI(M), LCI(G), LSM(R), and LCS(L). Only the LCS(L) cannot go into amphibious task forces. It's like it's classed along with barges instead of with the ocean going landing ships.