The industry standard gun lubricant is Break-Free CLP. It facilitates firearm maintenance, lubricates the gun, and aids in corrosion prevention. All across the world, militaries and police forces employ it.
Grease performs better than oil on any weapon component that experiences significant wear. Grease, not oil, the area if you see where the bluing has been removed due to metal-on-metal friction. I use Break-Free more than anything else these days.