Lithium and hydrogen bonded complexes of LiF and HF with H2CO, H2CS and H2CSe have been investigated using higher level ab initio calculations. Extensive searches of the potential energy surfaces for equilibrium structures have been done at the Hartree-Fock level, and post Hartree-Fock calculations at MP2, MP4 levels and DFT calculations with B3LYP functional have been performed on the stable forms. 6-311++G(d,p) and 6-31++G(d,p) basis sets on H, C, O, and S and 6-311++G(d,p) basis set on Se have been employed throughout. NBO analysis of the wave functions have been done to trade the origin of various interactions that stabilize the complexes. Harmonic frequencies computed at Hartree-Fock level show that, of the 10 proposed structures, LiF and HF complexes have three and one stable forms, respectively. Potential energy surface features, structure, and stability of LiF complexes are completely different from those of HF complexes. Though it is commonly observed that lithium and hydrogen bonding interactions stabilize the complexes, the origin and nature of them is found to be different in each form and in each complex. This is well reflected in complex geometries and energetics.