New Parts L are common materials in Xenoblade Chronicles. They are dropped by M87/GRANDs, Exterminator/EMBERs, and M97/CYCLEs in Agniratha. No one has them available for trade. They can be obtained from enemies north of Helas Pillar on the first floor of Agniratha.
Three of them are required for the quest Agniratha Beautification 2.