I have a Roku 3 that has started glitching/lagging in a similar way as mentioned here. From my phone, I would Airplay a cable tv app using Airplay & HomeKit on the Roku. Unfortunately, the show would play for 2-3 seconds and then pause for 1-2 seconds, before resuming and repeating. Very annoying way to watch television. The problem can be "solved" by pausing the tv stream to allow the video to "catch up". In this method, the video will play smoothly until reaching live stream.
This issue only started *after* the software update on 21 April. I have called the ISP and TV app providers. I have done resets for all devices including my iPhone, the Roku, and the modem. All software for all devices is up to date. The internet is not the issue as it works for streaming on phone and computer. The TV app is only partly the issue as it works on phone and computer. Airplay is not the issue because I can airplay YouTube videos to the tv. For some reason, the tv shows are too high of a bitrate for the Roku processor to handle (loosely paraphrased quote from the TV tech support person.) I will also mention that there was quite a bit of snobbery from the individual when I said I had a Roku. I can't count the number of times he said "we don't support Roku - there's a reason why."
I would like to see a prompt solution to this issue. I would like to prove the TV tech support person and the rest of the world wrong that Roku is not a joke, that it is not inferior to all the other streaming products available.