The main role of a dictionary is to provide information. For words like caenum, there are two different pieces of information that may be useful:
Spellings like coenum are commonly found
Certain individuals consider spellings like coenum to be "incorrect", for various reasons (convention, etymology, and analogy are common criteria for the "correctness" of spelling). As Expedito Bipes says, there is no simple definition of "misspelling".
Giving a common "mis"spelling along with a clarifying comment such as "less correctly" is I think intended to be a way of communicating both pieces of information. If the "mis"spelling was not listed by the dictionary, then the reader might wonder if "coenum" was a distinct word that just didn't happen to be in the dictionary, or if it was a "valid" variant spelling of caenum that had been accidentally omitted. If the spelling was listed in the dictionary without comment, then the reader might mistakenly assume that it was a "valid" alternative spelling.
That said, the brief and formulaic nature of this comment seems to leave its meaning a bit unclear. I haven't been able to identify the precise criteria used in L&S for determining when to use "less correctly" or "not" when discussing spellings.
My guess is that the specific phrase "less correctly" was just chosen as a kind of hedge because some people might consider some non-etymological spellings to be acceptable (due to established custom) or at least not entirely erroneous. Calling a spelling "completely incorrect" or "just a medieval misspelling" might be incorrectly understood as implying that it never had any common currency in Latin texts written by educated individuals, or that it only occurred accidentally or sporadically. In fact, it seems that many of the spellings that are described as "less correct" in L&S were in frequent use, possibly even up until the time that dictionary was being edited.
I have found an interesting review of "Harper's Latin Dictionary" in The Nation No. 762 (Feb. 5, 1880) that supports Expedito Bipes's statement that in the 19th century, the standardization of Latin spelling and codification of what was considered "correct" and "incorrect" was still in progress (but evidently, some individuals such as the author of the following quote were very interested in speeding up this process):
The features of the old dictionary [Andrews's Lexicon] which called most urgently for reform were the orthography and the etymologies. [...] The spelling of the new work leaves not very much to be desired, and it is a real comfort to see at last in a dictionary caelum, paenitet, cena, erus, umerus, umidus, nuntius, contio, condicio, incoho, and many others. This is not a minor point. It has at last dawned on the scholastic mind that there is a right way of writing (and pronouncing) every Latin word; and it becomes an important duty to free the language from the distortions brought about by a vicious mediæval pronunciation, and to accustom learners from the outset to the right forms of words. Often bad forms should have been rejected more positively: thus "contio (less correctly concio)." Why not "incorrectly"? On what principle the editors have given abicio, conicio, proicio, etc., at the heads of articles, and on the other hand "adjicio (better adicio)," we are at a loss to say.