Living Rulebook Edition

LRB Living Rulebook Edition 2003

No permission to download
This is the edition that is/was hosted on the GW site. Doesn't have the catch fire rules included, and introduces House Weapons Lists. These two inclusions/omissions are quite divisive amongst the game playing population, so I've rated one star lower for each of those. But apart from that, it's the Necromunda you remember from your youth, and love for its brutal awesomeness!
People that favour the LRB to the ORB or the NCE, tend to do so (in my honest opinion) based on their attachment to minor omissions or rule changes in the other two rulebook editions.

What they don't always see is the staggering amount of ambigious and unclear wordings in it, that makes gameplay an endless string of house rules and arguments.

My suggestion would be to use the NCE as a base ruleset, and add in the stuff from the LRB that you feel is missing (for instance if you really want that 60" Grenade Launcher").
Classic Necromunda with a few updates from GW - to me, helped smooth out some rules.