To clarify: Do you mean towards your FAA CPL or your EASA CPL?
For FAA the answer is yes as a LSA also falls under the Aircraft - Airplane - Single Engine Land Category.
For the EASA I can't say as the defintion for PIC time is different than the FAA definition and so might be LSA as this class does not exist in EASA land. (I would be happy to know the answer as well)
