I mean maybe we still are and my ignorance is showing. But I feel like we are no longer at an era to marvel at the "Magical Miracles of the Classical World" I feel like we could easily synthesize Greek Fire if we wanted to even. So, is the recipe for Greek Fire really lost to the world? No theories, or experiments in synthesizing it, just to say we could again?
The problem isn't really that we're bad at chemistry. "Greek Fire" has been used to describe multiple weapons, some evolutions of each other, some completely unrelated and mislabelled by clueless witnesses.¹
There's been plenty of experiments in modern times, from at least the 1930s², and for the main development line of "real" Greek Fire as far as we can tell, we've narrowed it down to some form of petroleum product plus some compound to thicken it³, and they generally work as described in reliable sources.
But we can't nail down which of the possible candidate mixtures was used in what instance, since the descriptions are too vague. If we ever found any, we could probably determine the exact recipe (at least for that point in Byzantine history) in short order, but until then it'll remain vague.
Either way it's just a historic curiosity and has no relevance for warfare, as napalm and derivatives are far superior (and wooden ships a somewhat rare sights on modern battlefields), so there's not exactly a huge effort put into making modern Greek Fire.
¹ https://www.jstor.org/stable/3106585?origin=crossref&seq=1
² https://pubs.acs.org/doi/abs/10.1021/ed014p360
³ http://channel.nationalgeographic.com/channel/the-link/videos/greek-fire/