Film strength -- property of a lubricant that acts to prevent scuffing or scoring of metal parts.
WD-40 and LPS, and other similar products, are not lubricating oils. They are penetrants and protective products that are designed to work their way into the smallest of crevasses, displace water (spray WD-40 on your wet automobile ignition wires), and surface protectants to bar oxygen in the air from coming in contact with ferrous surfaces (precision tools) to prevent rust. They have very little film strength and they will not produce an oil wedge in rotating machinery at any useful load.
O ring chains are prelubed at the critical wear pivots and the orings normally prevent loss of this lube. They also prevent renewing this lube. Penetrant oils will seep past the orings as they are not a perfect seal and dilute or interfere with the film strength provided by the factory lube. I would expect this to shorten the chain life.
Standard non-oring chains could benefit from a good cleaning and treatment of WD-40, particularly if the chain has been subjected to a water wash or operation in wet weather. WD-40 would displace any water under the rollers and other wear points. However, the lack of film strength offered by WD-40 would necessitate the follow up of a good penetrating chain lube to get under the rollers and provide a longer lasting wear preventative.
My chains are all of the standard type. I've been using black label PJ1 with good results. For minimum mess, it is best to apply it at the end of a days ride, preferably when the chain is hot. This minimizes fly off. PJ1 has tough lube suspended in a penetrative solvent that goes on thin and flows into minute crevases. The thin solvents will evaporate overnight, leaving the tough lube behind right where you need it. If you put it on right before a ride, centrifugal force will throw a lot of it off the chain where it will do no good.
For chain cleaning as well as cleaning any lube fly off, I use mineral spirits. (Hardware store, often labeled paint thinner.)
It is my understanding that chain wax works well for O Ring chains. It keeps the chain from rusting, is relatively dry so it won't attract dirt, and doesn't interfere or dilute the lube supplied by the chain provider. I think it dries faster, too, which minimizes fly off.
Cheers,