Even if L stopping WW3 is as simple as Churchill stopping WW3, Lunge doesn't compare to a guy that has actual international feats and statements. Lunge doesn't have the leadership capabilities or level of Churchill stopping WW3, since we don't have context of the extent of cases that he solved. That just means L is a different and better detective than Lunge.
Lunge doesn't have the intelligence of multiple intelligence agencies like L. And
intelligence agencies use their intelligence for internationally diplomatic, economic, and military defense. If L has intelligence of multiple intelligence agencies, he would be capable of doing the stuff intelligence agencies do, but several times better.
- This is relevant in this case of L v Johan since L can use the internationally diplomatic aspect of multiple intelligence agencies to engage with the international borders of Germany and deal with Johan's political mastery over Germany.
- Since Lunge has no feats or statements I know of so far that deal with international political stuff like intelligence agencies doing international diplomacy, that means that Lunge isn't comparable to L.
And since I stated in the previous second and third paragraph of this spoiler that Lunge doesn't have useful information or skill like having the intelligence of multiple intelligence agencies or useful leadership skills like Churchill. And Johan has outsmarted the guy, that means Johan hasn't outsmarted a person that has better useful intelligence than Lunge.
Not to mention that his statement of having several years of countless cases he's never left unsolved is a vague statement. Considering that
we have no context to the extent of the stuff he's solved so far in this debate, and could just be simple, not very impressive cases like solving a murder case.
Lunge also seems to work more out in the open than L, that would make Lunge more vulnerable to Johan since Johan is more likely to walk up to Lunge and tell the latter to "commit not live".
L doesn't work out in the open regularly and prefers to send a another person in as his public face.