How can I lower the playback preview resolution

Never figured that out yet. 4k lets you go down to 1/8. 1080p lets you go to 1/4 and 720 p only lets you go to 1/2. Doesn't really make sense. The best thing you can do is create proxys. Do some research and watch a youtube video on premiere proxys. Changing the video preview resolution in the sequence settings does not change your playback resolution. That is for  video that you render out in the sequence. Notice the colored bar above you footage on the sequence. If its yellow its not renderable (Technically it is but ignore that because its confusing) If its red it means that there are some effects you added that may need rendered out depending on your computer specs. Either press enter/return on your keyboard or go to sequence in the top of your screen and click render. The red bar should be green when done. That video that just rendered was saved as a "video preview" within a folder on your hard drive and the file resolution is based on that video preview settings in the sequence settings. Change it to 1280x720 and any video you render will save itself in the resolution. Change it to 1920x1080p and the video is saved with those specs. It doesnt do anything to footage on your timeline that has a yellow bar. The only way to actually have your footage playback in a lower resolution other than changing it to 1/2, 1/4, 1/8, and 1,16 is to create proxys like I was originally saying. 

Omg I keep replying to the wrong anser smh

The available options depend on the type of footage used.

Better than reducing Playback Resolution, however, is using proxies.  Choose Cineform.

Work offline using proxy media |

You can lower resolution of the preview codec in the sequence settings but thats it.