My .02:
The weather deck on the Iowa class, as seen, is covered by wood:
Underneath the wood (and it was a nice couple inches thick) was 1.5 inches of special treatment steel (STS, something up to 2x harder to penentrate than normal armor steel). Any shell, bomb or missile (maybe excluding bunker-busters) would detonate on this deck, and probably drill a hole in it. That's why the next deck was armored, and measured 6 inches in thickness, including over an inch of STS (a CD-ROM is about 4.7 inches in diameter, to show the scale). That way the explosion of the projectile that hit the weather deck would have a whole 7-8 feet of air to loose it's shockwave before even touching the armor.
Also- stuff hitting a bunch of wood backed by STS could bounce off or skid across it, and that's why there is only 7.5 inches of steel, configured to create 'spaced armor' protecting the top of the ship. If anything was powerfull enough to cause the armor deck to shatter and throw pieces of metal around, there was the splinter deck, .625 inches thick to stop the debris.
Now for the hard part- low angle projectiles.
These are to be decapped (WW II AP shells had an armor piercing 'cap' on the nose to better drill through battleship belts) or detonated (more modern stuff) on a layer of STS, and then the de-capped shell, or explosion would fly through an outboard room inside the ship. After doing that, it would hit the 12.1 inch thick belt (again with some STS on it), that was inclined 19 degrees to deflect some of the energy that was hitting it.
Protection against torpedoes is another, long story. Whoever wants to find out can go ahead and read about it.
How does modern warship armor look like?
P.S. Comparing the Lilith to a monitor is a good idea. The HMS Abercrombie was 102 meters long, had battleship guns and cruiser armor, at the cost of a 6 knot max speed.