In a manner that is deadly, fatal, or extremely dangerous.
From 'deadly' (capable of causing death) plus the adverbial suffix '-ly' (manner). The word evolved from Old English 'deaþlic' meaning 'subject to death' or 'mortal,' with the adverbial form indicating how something is done in a deadly way.
English adds '-ly' to nearly any adjective to make an adverb, and 'deadlily' follows this pattern—but it's so rare in modern usage that many people would call it archaic, showing how some grammatically correct words just fade from practice.
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