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Longitude by lunar altitudes was invented and debated at least 250 years ago. It has been rediscovered many, many times since then and dismissed again and again, too. There was an article in MNRAS by a Lieutenant Ashe of the Royal Navy in 1849 describing his pleasure in discovering this method and noting that it might be more practical than longitude by lunar distances. The article is interesting primarily not for his calculational method, which looks like the long way around to me, but for his introductory comments and the editor's notes at the end. In the intro, Ashe mentions that he has seen the chronometers checked by lunar distances only once in his twenty years of experience at sea, which is good evidence on the era when they had fallen out of use. Like far too many commentators, Ashe assumes that this was because lunar distance calculations were too difficult (this was definitely not the case). At the end of the article, the "editor" (possibly G. B. Airy himself) notes that the problem with longitude by lunar altitudes is intrinsic: the horizon can't be trusted and the Moon's motion along its orbit is inclined relative to the horizon. I don't feel I have the time to keyboard this, but the comments are relevant, so I'm going to cheat and attach the text as an image file.