I don't know the proverb, but I am sure that, in your second version, "lia" is a mistake for "lla" or "li ha", that means: "he has".
Toscan dialect must express the subject, in pronominal form, even when it appears as a noun. Very similar to English language. So the translation is something like: "the cock it has long wings. "Li" or "ll" stands for "egli" that means "he"; "a" stands for "ha" has. Lia > lla or li a = li ha, egli ha 'he has'.
From a quick check in the web, I found different proverbs in many Italian dialects, that mean: "from the 21 December (or about) the daylight start to get longer and longer". The most similar to your proverb is "Per San Tommé il giorno allunga quanto il gallo alza il pié": for Saint Thomas the day becomes longer as much as the cock rises its feet".