Various old dictionaries seek to explain this medical term for sore eyes through a variety of others that are at least as obscure. To equate it with blearedness, glama, or epiphora would seem, at least to us today, to be ill-judged attempts to clarify the matter.
Blearedness, although an uncommon word, may be converted without great effort to the more common bleary-eyed. But glama doesn’t even appear in the Oxford English Dictionary, so it’s lucky that my 1913 edition of Webster does include it, defining it as “a copious gummy secretion of the humor of the eyelids, in consequence of some disorder”, adding helpfully that it is from Latin gramiae. The Oxford Latin Dictionary glosses this as “rheum in the eye”, rheum in its turn being a watery fluid that collects in or drips from the nose or eyes, borrowed from Greek rhein, to flow. Epiphora is still in the medical vocabulary, though hardly known outside the profession, and means “an excessive watering of the eye”. One big medical dictionary that I consulted cross-referenced epiphora to tearing, which disconcerted me until I realised the latter word should be rhymed with fearing, not bearing.
Lippitude arrived in English in the early seventeenth century, probably from a French word that had been created from the Latin lippus, blear-eyed. It seems to have gone out of use in the 1850s.