I carry chamber empty, hammer down. If a shot is likely, I carry round chambered, hammer on half cock(lowered all the way, then drawn to half cock). I think it is dangerous to leave a hamer down on a chambered round, an impact or jarring of the gun could fire it.
I DON'T carry chamber empty with the hammer on half cock. The trigger or sear notch in the hammer CAN be broken by a very hard pull on the trigger or an impact on the hammer. If the chamber is empty, there is no reason to have it on half cock, and is inviting breakage if dropped. Certainly not "improving" safety. I use the hammer condition as a quick chamber staus check. If down, it's empty, if half cock, it's loaded. I've used this method for 25 years or so and had no problems. Most of my guns have been loaded (magazine, not chamber) for as long as I've owned them, unless travelling in a state that doesn't allow transport while loaded. All my levers are standard guns, no rebounding hammer or cross bolt safeties.
The "lever safety" on some guns isn't a true safety. I believe it was designed keep the gun from being fired when the action is unlocked, it would be very unhealthy to fire a round with the gun unlocked. I don't think it should be regarded as a "safety" per se. Blocking the trigger will not neccesarily prevent the gun from firing if the hammer is struck hard enough to shear the half cock notch. Many of the guns with this lever block have a strong enough lever latch to keep the lever all the way up when it's closed, and I think this is as it should be. Winchester 1886's and 1892's don't have this lever "safety", they have a part on the tip of the lever that retracts the firing pin before the locking bolts lower. No "lever safety" was required. Are they "less safe"? I don't feel so.
As many have said, the most important thing is not ever pointing the gun at anything you don't want to shoot.