What is the linguistic relationship, if any, between the Latin word luna and the biblical Hebrew word לבנה, which are phonetically similar and both mean "moon"?
Most likely they're unrelated.
Latin lūna "moon" comes from Old Latin losna from PIE *lowks-neh₂, derived from *lewk- "bright, shining".
Hebrew l'vaná "moon" comes from the feminine of laván "white". I'm unsure where that goes back to in Proto-Semitic, but it seems to be a native Semitic root because it also appears in Arabic laban "milk".
It's not impossible that one influenced the other, but they seem to have unrelated etymologies. Interestingly enough, they both come from a feminine form of an adjective describing the moon.