Almost any size round can be lethal if used right. As someone else posted, the AR-15 (an excellent gun) uses a .223 round and it is a highly lethal weapon. However, if you shoot someone with a .22 short round from a short barrel pistol, well you might as well beat them over the head with the pistol. It will probably be more effective.
A bigger round, like a .44 magnum, a .45 ACP, or a .50 caliber will almost always stop someone dead in their tracks. A smaller, high velocity round like a 9mm can go straight through someone without them even realizing they've been shot (for a while anyway).
But I also subscribe to the school of thought that says I'd rather carry a .25 than nothing at all.
The Israeli El Al airline security officers assigned to that detail by the General Security Services [ShinBet] thought otherwise, and found the reduced loads used in their .22 Berettas [loaded in .22 long rifle cartridge cases for feeding through the pistols magazines, but at .22 short velocity levels] were quite okay. I had the chance to shoot with a couple of those operators, who thought that shooting off a 500-round box of ammo was a good warmup, and that my Browning GP was unnecessarily noisy. A few also used the .22 short chambered Astra model 2000 *cub* as a backup handgun; the little Astra makes even a Walther PPK look large by comparison; I used to keep one as a backup in my handcuff case. But again, you have to practice with it to get the desired result.
There's at least one recorded case of an elephant being killed by a .22 short. And do not ever think that if such a weapon is pointed your way that your life is not in danger.