I'm sorry but .22lr guns don't get lead fouling period. Once about 5 rounds have been fired the barrel is lubed as well as it needs to be from the ammo alone. The boresnake does not even need oil on it as it is only for removing any solid matter like powder residue.
As for the dirty/clean question I can tell you from competition experience that when I used to clean them too often I found that to get the reliability back I had to take the gun to the range and put 50--100 rounds through it or it would have issues early in a match. Since I have stopped using regular gun oil and switched to light amounts of synthetic CLPs like Eezox or Militec-1, I no longer have to prerun the guns to get them ready, but I use very little lube. I treat my centerfire raceguns different, those I lube up because they have no problem powering through lots of lube, but rimfires often have issues. For instance the key to shooting in cold weather is keeping the ammo warm. If the bullet lube stays fluid the gun will continue to work.
If you want a gun to stay rust free use Eezox. Much better than WD-40. See the online testing if you have not previously.