Summary: We continue to study the simplest closure conditions for chains of spectral transformations of the Laurent biorthogonal polynomials (LBP) [cf. the authors, J. Comput. Appl. Math. 131, No. 1-2, 253–266 (2001; Zbl 1064.33017)]. It is shown that the 1-1-periodic \(q\)-closure condition leads to the LBP introduced by Pastro. We introduce classes of semi-classical and Laguerre-Hahn (LBP) associated to generic closure conditions of the chain of spectral transformations.