.22 Lugers are striker fired.
Also don't confuse the lack of a visible hammer with striker fired. Many of the guns that LOOK like striker fired guns actually have an internal hammer, and so are not striker fired guns.
I can so no advantage to a second strike capability in a rimfire pistol, and very little use to one in a center fire one.
My experience in the past half century is that if rimfire rounds don't fire, it is most often because there is no (or not enough to fire) priming compound inside the rim, where the firing pin hits it. Most "dud" .22 will fire when struck again, in a different spot on the rim. A "second strike" in the same spot as the first is unlikely to do any good.
In a center fire pistol, a second strike may be of some use, if the reason for failure to fire is an improperly seated primer. But if the reason is something else, its not likely to do anything more than go "click", again.
If YOU think second strike is important, by all means, get a gun that can do that. For me, its not a feature that matters.