That took quite a while. According to a tip sent from an Android Police reader, that very small sliver of Galaxy S4 owners which opted for the Google Play Edition of the phone (running stock AOSP software) is now receiving the Android 5.1 update. That's the one that first started coming out way back in February, at least to Nexus devices. Yeah, the Google Play Edition program isn't looking quite so hot these days, more's the pity.
According to our tipster, the OTA is coming in to update the S4 GPE from LRX21P (Android 5.0, circa November 2014) to LMY47O (released around April). Note that it's Android 5.1, not Android 5.1.1, the latest public release of the platform. Yeah. If I paid $600+ to get an off-contract version of a phone with "Nexus-style updates," I'd be pretty pissed too. We've got a link to the OTA ZIP file if you'd like to flash it manually: download it here.
Remember that these software updates need at least some input from the manufacturers themselves, and since neither Google nor Samsung seems all that interested in Google Play Edition hardware at this point, I'd say that we're unlikely to see too many more OTAs for these phones and tablets. We might be able to hope for a Marshmallow upgrade (eventually), but after that, I wouldn't be surprised to see OTAs stop. It's a good thing Google Play Edition devices have unlocked bootloaders...