I assume by "play lists", you mean YouTube's "watch later" videos? You can access this in the Roku's interface by pressing up and down on the remote. On the left side of the screen, you can scroll up and down among your available channels, search, watch later, etc. Watch later videos are one of the selections, and all of your watch later videos show up there.
Here's what it looks like on Roku:
You can click on one of the videos to watch it. Right now, the first video (highlighted in white) is the selected one. I can watch it, and then when finished, click the "
Look at the icons on the left of the screen. The Watch Later videos is selected (the clock icon). If you press up on the Roku remote, you go to that chat thing (which I never use). If you press down, you go to the search (magnifying glass). Press down again from it and you get settings (gear), etc. The five icons near the bottom (and more under those, too, if you scroll that far down) are the icons for channels to which I'm subscribed.