To go along with the "mourning" words, a generic phrase to acknowledge the fact that someone is mourning a loss... along the line of "my condolences" or "I'm sorry for your loss", etc.

lowitheláad -- to feel, as if directly, another's feelings (pain/joy/ anger/grief/surprise/ etc.); to be empathetic, without the separation implied in empathy [lo + with=person + láad=to perceive]

óom -- to mourn