Shooting lead bullets will not damage or break your gun. Lead bullets will not harm your barrel, even if oversized. Even if they are hard cast, which is a fancy way of saying they are an alloy (mix of lead, tin, and antimony) they will put less stress on your gun than jacketed bullets.
Lead bullets require a different approach than jacketed, because they function drastically differently when going down the barrel. With a jacketed bullet, the lead core is protected from the barrel by the copper jacket, which is much harder and resisst deformation. A lead bullet is incredibly malleable. So much so that in a upon firing the base accelerates before the nose starts moving. This creates a gas seal at the base of the bullet that prevents the super-hot burning plasma from shooting between the bullet and the barrel.
THAT is the main reason that you want a larger diameter bullet...to act as a gas seal. If the bullet is too small in diameter, the gas will cut the sides of the bullet and escape down the barrel.
Why does that matter?
1. You are getting an inefficient burn of your propellant. Think of it like an old engine that needs new rings on the pistons...smokey, poor mileage, inefficient burn.
2. It damages the bullet. This leads to poor accuracy at the target.
3. The hot gas will microscopically melt the lead and iron it into place. This is the main cause of leading when shooting cast bullets.
So we have established that lead needs to be a larger diameter than your barrel. How big is too big? If the round won't chamber...it is too big. I have never seen a 9mm that would not chamber a .358" bullet.
Does the larger bullet cause an increase in pressure? Almost certainly. But why? Is it because the bullet has more pressure exerted on it upon obduration? Or does it build more pressure due to a more efficient combustion? Maybe a little bit of both. But how much more pressure? A barely discernable amount.
Now if you were talking about JACKETED bullets...then yes, a safe load could have a large increase in pressure from going up just 0.001" in diameter. You would not want to shoot .357" JACKETED bullets in a 9mm, but lead bullets are just fine.