This is a pretty popular meme from a while back that started with this image
and has had quite the bit of spread on places like iFunny and Twitter.
Google images has shown quite a few examples of this:
so it's really weird that it never got an article on the site. Since I'm more or less terrible at researching memes unless they're from YouTube, I think it'd be best if someone who's more experienced in that department take care of the research. However, I would suggest looking at iFunny in particular as that site seems to be the origin of this meme(judging by the original image at the top's watermark)
The Way iShowSpeed Purses His Lips In His 'Phone GIF' Is More Expressive Than Any Emoji Could Ever Be