Full configuration interaction (FCI) has been used in conjunction with the lithium [6s5p3d1f] (Iron, M. A.; et al. Mol. Phys. 2004, 101, 1345) and hydrogen aug-cc-pVTZ basis sets to construct an 83-point potential energy surface of the (1)A(1) ground state of (LiH2+)-Li-7. Vibrational and rovibrational wave functions of the(6,7)LiH(2)(+), (LiHD+)-Li-6,7, and (LiD2+)-Li-6,7 ground states were calculated variationally using an Eckart-Watson Hamiltonian. For (LiD2+)-Li-7, rovibrational transition frequencies for K = 0, 1, 2 and J <= 10 are within ca. 0.1% of recent experimental values (Thompson, C. D.; et al. J. Chem. Phys. 2006, 125, 044310). A 47-point FCI dipole moment surface was embedded in the rovibrational Hamiltonian to calculate vibrational and rovibrational radiative properties. At 296 K, with v <= 4 and J <= 4, the 2(02) <-3(03) rotational transition in the \001 > band was found to have the greatest spectral intensity with respect to the ground electronic states of (LiH2+)-Li-6,7, (LiHD+)-Li-6,7, and (LiD2+)-Li-6,7. In each case, the most intense rovibrational transitions have been assigned unequivocally using the J, K-a, K-c assignment scheme.