Lysosomal serine protease with tripeptidyl-peptidase I activity (PubMed:11054422, PubMed:19038966, PubMed:19038967). May act as a non-specific lysosomal peptidase which generates tripeptides from the breakdown products produced by lysosomal proteinases (PubMed:11054422, PubMed:19038966, PubMed:19038967). Requires substrates with an unsubstituted N-terminus (PubMed:19038966). {ECO:0000269|PubMed:11054422, ECO:0000269|PubMed:19038966, ECO:0000269|PubMed:19038967}. This is the function of TPP1 (tripeptidyl peptidase 1, Ensembl gene identifier ENSG00000166340).