Yes, I know American dictionaries list "firstly," just as they list "ain't" and "snuck." They record "dove" as an alternative for "dived," "buffalo" as a popular but unscientific word for the American bison, and "lay" as a synonym for "lie." They register the increasingly common enunciation of the silent T in "often" and the silent C in "arctic." English is a democratic language, not an authoritarian one. The purpose of a German or French dictionary is to tell the user how to speak and write German or French properly. The purpose of an English dictionary is to help the user understand the chaotic variations of the language that they are likely to encounter in the absence of any authority. Nonetheless, "firstly" is regarded by most editors as bad English and "secondly" is regarded by virtually all editors as utterly wretched English. The distinction you point out between "lastly" and "finally" is accurate, but the same distinction holds if you use the preferred word "last," which, like "first" and "second," functions as both adjective and adverb in proper English. John and Mary live within walking distance of the theater so they arrived first. I had to drive in from the suburbs and there was an accident on the freeway, so I arrived last and was almost late. No one would think of using "firstly" and "lastly" in those sentences. So why use them ever?