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The lesser restoration spell description states:

You touch a creature and can end either one disease or one condition afflicting it. The condition can be blinded, deafened, paralyzed, or poisoned.

The description of greater restoration says:

You imbue a creature you touch with positive energy to undo a debilitating effect. You can reduce the target’s exhaustion level by one, or end one of the following effects on the target:

• One effect that charmed or petrified the target


• One curse, including the target’s attunement to a cursed magic item


• Any reduction to one of the target’s ability scores


• One effect reducing the target’s hit point maximum

But, on DMG page 260, under "Curing Madness", it says:

A calm emotions spell can suppress the effects of madness, while a lesser restoration spell can rid a character of a short-term or long-term madness. Depending on the source of the madness, remove curse or dispel evil and good might also prove effective. A greater restoration spell or more powerful magic is required to rid a character of indefinite madness.

Normally, the ruling is that specific takes precedence over general, but these are both pretty specific; additionally, this flies directly in the face of the concept of "spells do exactly what they say they do and nothing more", because both of these spells have an additional condition effect they can remove that isn't specified in the PHB at all.

So, as I put it in the title: Do casters know that these spells can cure madness? Or is this information excluded intentionally?

Additive, Not Exclusive

To address the first point... You have two specific sets of rules, but they don't conflict. The spells have a list of things they can do. The optional Madness rules add to the scope of the spells. You'll find other features scattered through the game (particularly in the Monster Manual) that say "This effect can be removed by ______."

While the Restoration spells don't natively say they're effective, other abilities can add to the capabilities of the spells. However, without some sort of supporting text, the Restoration spells are limited to the text of the spell itself.

Character Knowledge

The rules don't address it either way. Most DMs assume characters to be competent adventurers, familiar with the tools and techniques their class provides them.

Think of the characters like you would people. If this brand of deep madness is new to the characters or the society they come from, they very well might not know. In the very same game, you could conceivably have a character who's background story indicates experience within a sanitorium or asylum and that specific character would know. You could also abstract it with Arcana checks, if you'd like - base the DC on how obscure the whole concept of madness is in the world.