How can I achieve this lo-fi laggy extreme camera shake effect in After Effects or Premiere?
OMG strobe! That's what the "laggy" effect is; it was very popular with "experimental" film school students back in the nineties. It went the way of lens flares and the posterisation effect; some would say it is better left in its tomb, but that's a matter of personal taste.



If you slow down the video you'll see what's going on, the apparent frame rate is slowed down to four or five frames a second, destroying the illusion of smooth motion. In the nineties, to achieve the long exposures that give the light trails and motion-blur you had to shoot on a film camera that could do variable frame rates; these days a lot of digital cameras can do it. You can lower the frame rate in post, but you won't get the trails and motion blur. Here's how to do it in After Effects.

You need to find a camera that can shoot at a frame rate to around 4-10fps, and that lets you adjust the shutter speed to give you as long an exposure as possible. Then, as you said, go nuts shaking the camera around. Your audience will thank you /s.