We performed a spectroscopic survey toward five intermediate-mass class I YSOs located in the Southern Vela molecular cloud in the L and M bands at resolving powers 600-800 up to 10,000, using the Infrared Spectrometer and Array Camera mounted on the VLT-ANTU. Lower mass companion objects were observed simultaneously in both bands. Solid H2O at 3 micron is detected in all sources, including the companion objects. CO ice at 4.67 micron is detected in a few main targets and one companion object. One object (LLN 19) shows little CO ice but strong gas-phase CO ro-vibrational lines in absorption. The CO ice profiles are different from source to source. The amount of water ice and CO ice trapped in a water-rich mantle may correlate with the flux ratio at 12 and 25 micron. The abundance of H2O-rich CO likely correlates with that of water ice. A weak feature at 3.54 mu attributed to solid CH3OH and a broad feature near 4.62 mu are observed toward LLN17, but not toward the other sources. The derived abundances of solid CH3OH and OCN- are ~10% and ~1% of the H2O ice abundance respectively. The H2O optical depths do not show an increase with envelope mass, nor do they show lower values for the companion objects compared with the main protostar. The line-of-sight CO ice abundance does not correlate with the source bolometric luminosity. Comparison of the solid CO profile toward LLN17, which shows an extremely broad CO ice feature, and that of its lower mass companion at a few thousand AU, which exhibits a narrow profile, together with the detection of OCN- toward LLN17 provide direct evidences for local thermal processing of the ice.