It's an age-old concept of humans to consider the left side to be in some way inferior to the right side. I don't know whether it's the case in all cultures, but at least in the Indoeuropean languages also the words used for left and right very often have additional meanings, and I assume the reason is more instinctive than cultural. "Sinister" and "laevus" for example are the Latin words for "left", but they also mean "wrong", "bad" etc., whereas the word for "right", namely "dexter", also means "rightful", "proper", "dexterous".
The anthropological reason for such connotations might be that for most humans the right hand is the one they use mainly. That has developed to cultural specifications like the Hinduistic tradition to use only the right hand for eating and only the left hand when going to the toilet. Biologically I guess using the right side as the more active one has the advantage that it allows the side where the heart is on to be more passive and thereby more protected. And well, using separate hands for eating and for cleaning also has biological advantages.
It however is not the case that the words for left always only have negative meanings and words for right only have positive meanings, there exist counter examples as well.
Regarding the LHP, or vama-marga, it's not completely clear where this Sanskrit name comes from exactly since also this Sanskrit word "vama", meaning "left", has many other meanings, just look:
http://spokensanskrit.de/index.php?script=HK&beginning=0+&tinput=vAma+&trans=Translate&direction=AU
So, the name of the vama-marga is not a biblical reference, they are related on a deeper level if at all.
One could however argue that the fact that "LHP" was adopted as a term by us westerners and nowadays is used as a quasi-synonym for Satanism was supported by our own cultural connotations with the left side.