The “rules” under which hyphens are used to connect multiple modifiers, like “well(-)known man,” are varied and difficult to remember. Some style guides try to avoid hyphens except when their absence would create confusion: Don’t hyphenate “local business owner,” for example, but do hyphenate “small-business owner,” since it could be read that either the business or the owner is small. Others suggest hyphenating most of these compound modifiers for consistency: “mental-health officials.” For our man of renown, some style guides call for a “well-known man” before the noun, but “as a man, he is well known,” with the compound following the noun. (We’ll deal with that another time.)
That may be confusing enough. So many people take solace in the all-but-universal “rule” to not hyphenate an adverb ending with “-ly.” She had an “illegally issued license,” not an “illegally-issued” one.
But explanations of why to shun that hyphen are rare, as are acknowledgments that, as with most “rules” of English, there are exceptions. (We’re going to be simplifying the grammar a bit here, but the principle’s the thing.)
Part of the reasoning for not using a hyphen after “-ly” adverbs is that, appearing before a verb as it does, an “-ly” adverb is obviously attached to it, so no confusion is possible. As The Chicago Manual of Style says: “Compounds formed by an adverb ending in ly plus an adjective or participle (such as largely irrelevant or smartly dressed) are not hyphenated either before or after a noun, since ambiguity is virtually impossible. (The ly ending with adverbs signals to the reader that the next word will be another modifier, not a noun.)”
However, in the absence of knowledge that can be used to determine an outcome based on logic, “rules” become the rule. Since many people cannot point out which words are the adverbs and which the adjectives, or even identify “modifiers,” they blindly refuse to hyphenate any “-ly” word.
And thus confusion arises.
As Chicago notes, “not every word ending in -ly is an adverb—some are adjectives (e.g., lovely, curly).” Those might take hyphens in compounds to avoid confusion: “The curly-haired girl” means the girl’s hair is curly, not the girl herself. (She might be “curvy,” though.) Other modifier pileups might or might not take hyphens, depending on whether they are compounds or just two modifiers. “The large green box” takes no hyphens, because both “large” and “green” refer to the box; “the large greenish-blue box” needs a hyphen because “greenish” is referring only to “blue,” not the box. (Do you need a comma between “large” and “blue” or “greenish-blue”? Maybe: We’ll discuss that another time as well.)
Some adverbs not ending in “-ly” do need hyphens, and some don’t. “A very green box” doesn’t need one between “very” and “green,” because no one would mistake “very” as being anything other than a modifier of what follows. But “a tomorrow-ready missile shield” needs one between the adverb “tomorrow” and the verb “ready” because “tomorrow” can be a noun as well, and the reader needs a signal that it’s not a noun in this case.
But there are times when a “ly” adverb does need a hyphen. As Chicago notes, the adverb in “a sharply worded reprimand” does not take a hyphen, but the one in “a not-so-sharply-worded reprimand” does. The adverb itself isn’t taking a hyphen, but the whole phrase “not-so-sharply-worded” is a gigantic adjective.
These phrases are called “phrasal adjectives” by grammarians; we can just call them “compound modifiers.”