Let G be a finite group and \(a^G\) be the conjugacy class of \(a\in G\) . The commuting conjugacy class graph of G is a simple undirected graph, denoted by \(\Gamma _G\) , whose vertex set is \(\{a^G : a \in G\}\) and two distinct vertices \(a^G\) and \(b^G\) are adjacent if there exist \(x\in a^G\) and \(y\in b^G\) such that x and y commute. In this paper, we compute distance Laplacian spectrum and energy of \(\Gamma _G\) if G is isomorphic to \(D_{2n}\) (dihedral group), \(T_{4n}\) (dicyclic group), \(U_{(n,m)}=\langle x,y:~x^{2n}=y^m=1,~x^{-1}yx=y^{-1}\rangle \) , \(V_{8n}=\langle x,y:~x^{2n}=y^4=1,~yx=x^{-1}y^{-1},~y^{-1}x=x^{-1}y \rangle \) and \(SD_{8n}=\langle x,y:~x^{4n}=y^2=1,yxy=x^{2n-1}\rangle \) . We also consider finite groups whose central quotient is isomorphic to \(\mathbb {Z}_p \times \mathbb {Z}_p\) (for any prime p) or \(D_{2n}\) . Our computations reveal that the commuting conjugacy class graphs of the above mentioned groups are distance Laplacian integral.