Over the last 20 years or so, the consensus has grown in Indo-European linguistics that Proto-Indo-European had only the animate/inanimate distinction mentioned above. After the Anatolian branch and possibly Tocharian split off from the other Indo-European languages, the remaining core of IE languages developed the three genders masculine, feminine, and neuter.
The idea that Lithuanian is extremely conservative from a PIE perspective is rather outdated. Lithuanian does preserve a number of features of what might be termed “Proto-Nuclear-Indo-European” (to use the terminology of Lundvist & Yates), but the insights from the Anatolian languages show that not all of these features can be reconstructed back to Proto-Indo-European itself.
What is interesting, neither Lithuanian, nor Latvian has neuter gender. While slavic languages, like Russian or Polish, do have. To be fair, old Prussian seem to have had neuter gender. But given Germanic influence, they likely adapted in later days. It'd be weird if IE had developed 3rd gender, then Baltic languages dropped it while other languages around them did keep it.
Got any links or literature on how that evolved according to the new school?
It isn't at all strange that the East Baltic languages developed (along with other PNIE languages) the neuter and then dropped it later. The very same happened in Albanian, Irish, and the Romance languages (except for Balkan Romance).
Any recent introduction to IE linguistics starting from Beekes' Comparative Indo-European Linguistics will discuss the neuter being an innovation after the Anatolian languages broke off. However, I would especially recommend the Handbook of Comparative and Historical Indo-European Linguistics that will be published by Mouton de Gruyter this September, as it will contain a state-of-the-art survey of the field by a number of prominent scholars. See Lundvist & Yates' chapter on Morphology in it (you can also download a preprint PDF of this chapter from Yates' papers on Academia.edu if you have an account there).
If the neutral gender was dropped, I'd expect to be at least some leftovers... Anyway, I'll try to get hold of that book once it's out. Looks like it'd be interesting read.
Some people say Lithuanian has kept most of proto-Indo European features. If that's true, inanimate/neuter had to evolve later than gender split.