Recently I was doing some website proofreading and edited out a couple of hyphens that appeared after words ending in “ly.” Words ending this way are adverbs. If they precede an adjective, they combine to make a compound adjective and a hyphen is unnecessary. Why? Because no further clarification is needed. Examples: a “dimly lit room,” a “horrendously large blister,” a “finely tuned piano.”
Here is what the Chicago Manual of Style has to say on the subject:
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.) CMS, Section 7.86.
On the other hand, hyphens do appear in your everyday compound adjectives such as a” high-speed chase” or “well-intentioned remark,” and in a good many other places. So, using a hyphen properly can be challenging. You and your colleagues may have differing opinions on the best way to insert it, and some may decide to ignore it altogether. There are times when the use of a hyphen simply comes down to personal choice—or appears by mistake.
In The Elements of Style, noted wordsmiths Strunk and White give the example of a hyphen being used to considerable public amusement when two newspapers joined forces. The News and the Free Press became the Chattanooga News-Free Press. The hyphen, of course, made it sound as though readers who were looking for news items weren’t going to find any in that publication.