Could someone with a good cpu test my project? See if it lags?

I downloaded your project and it is not helped much by more CPU playing that timeline  I ran the project on both my laptop and my 8-core i7-5960X at 4.5 GHz and while it was slightly better than the frame loss it was not enough to be happy with that.  Both cases there were thousands of missing frames.  Both of my computers are all SSD so that did not help.  There is no GPU acceleration so no upgrade that way will do any good

Your green screen is a non-standard 490 x 360 resolution, I do not know if that could contribute to frame loss during playback.  I

Your media is MP4 that requires lots of CPU power, maybe if you converted to an easier codec like AVI you might find it better suite to your editing.   It of course does require more storage space but since it is native to Premiere it will be worthwhile to try that for your editing process, then you can always export back to MP4.

Before you change the CPU (It may very well be the issue), what are the rest of the specs of your computer, including your hard drive setup (how many, what kind, what is on each, and how full)?

What camera are you using?