According to the introduction, human L1 is located at Xq28, in the q arm of the X chromosome. It is also on the mouse X chromosome. The $CHL1^{-/-}$ nomenclature you've already figured out: a homozygous knockout of the CHL1 gene. I haven't thoroughly read the whole paper, but there must be some undesirable phenotype when L1 is homozygously knocked out in female (X/X) mice, so the researchers in this paper are using male (X/Y) mice, with L1 knocked out on the single X chromosome. There is no corresponding allele on the Y chromosome, so the nomenclature is $L1^{-/y}$.
This is borne out in the Materials and Methods:
The L1 gene is located on the X chromosome, and its deletion results in poor breeding capability of males and thus female mice homozygous null for the CHL1 gene and heterozygous for L1 ($CHL1^{-/-}$/$L1^{+/-}$; C57BL/6/Sv129, ∼9:1) were crossed with $CHL1^{-/-}$/$L1^{+/y}$ males (C57BL/6) to produce $CHL1^{-/-}$/$L1^{-/y}$ double mutants.