Get a scott oiler and lube it whenever it's running (which is when it NEEDS it, not after you STOP).
As for chains (O ring, X ring, or other ring) not needing lubing, I doubt triumph & the chain manufacturers would all jump up n down about it if they didn't. They come with lube in them from the factory but constant use will squeeze it out and it needs to be replaced... and the lube inside the links doesn't lube or clean the moving parts on the outside.
FYI, WD40 will penetrate the links and dilute the grease inside them, allowing it to be forced out more quickly, and will cause the O/X rings to perish and become brittle. Clean chains with diesel or kerosene (which both contain waxes which will protect the X/O rings), or a proprietary chain cleaner.
Wear of the chain & sprockets is only part of the reason for lubing the chain. Chains are made of about 104 links, which each contain two pivots. That's 208 moving metal parts. Without lube, the friction that builds up can seriously reduce the bike's performance. I've seen bikes that could barely be pushed due to rusted, un-lubed chains, and while that's an extreme case it does demonstrate how much power can be lost to a dry chain. Lubing also reduces noise and heat which are the first two signs of a worn or dry chain robbing power. (Noise and heat are forms of energy which has to come from somewhere. In this case they're converted from the kinetic energy the engine puts out, meaning less power to the wheel. Basic physics.)