Limited birthday distinguishers (LBDs) are widely used tools for thecryptanalysis of cryptographic permutations. In this paper we propose LBDs onseveral variants of thesLiSCPpermutation family that are building blocks of tworound 2 candidates of the NIST lightweight standardization process:SpixandSpoC.We improve the number of steps with respect to the previously known best results,that used rebound attack. We improve the techniques used for solving the middlepart, called inbound, and we relax the external conditions in order to extend theprevious attacks.The lower bound of the complexity of LBDs has been proved only against functions.In this paper, we prove for the first time the bound against permutations, whichshows that the known upper bounds are tight.