Old Geezer said:
Also, why are these lock types better than leaf or liner locks?
I'll give you my opinion, and you can take it for what its worth. The LAWKS is, as someone else already said, a linerlock safety device that keeps the lock from disengaging the tang of the knife. It isn't fool proof, and can fail with some effort, but its also not that bad. I don't discuss CS if I can help it. Ever.
As to why the Axis is better than liner locks, the opinion of many is that when the springs wear, they actually cause the lock bar to move further UP the tang, thus making the lock MORE secure over time. That, and the fact that in order to break the Axis you'd have to either sheer through the lock bar OR the steel liners gives many people a great sense of security.
For Frame Locks, opinions vary. One thought is that there is a worry amongst some that the hand can unintentionally move the liner off of the tang and cause the knife to close (thus things like LAWKS). With a framelock, your hand (and typically your palm) ride against the lock bar itself, and so the harder you squeeze the handle, the further up the tang ramp you drive the lock bar. Thus, the thought is that this is more secure than a straight linerlock.
FOR MYSELF, I choose to see locks as a safe-guard, but no replacement for general knife safety. A folding knife is, and always will be, a compromise. The best lock on a knife is a fixed blade (or Balisong). Just like I treat all guns as loaded and dangerous, I treat all knives as if they had no lock. My grandfather has carried razor sharp slipjoints all his life, and he still has all of his fingers. I attribute this to Technique over Technology.
Personally, I carry a framelock (Buck/Mayo 172) and a linerlock (Strider GB) every day, so I don't have any particular favorite. I would take a questionable lock-type from a good maker/company over a "superior" lock-type from a crappy maker any day as well.
Sorry for the length.