The first plan is a nice reproduction of Roy Underhill's lathe by Mike Adams. I found the plan of Mikes lathe on the web many years ago. Mike did a nice job of building Roy's lathe, and wrote and assembled an excellent 19 page pdf manual on the process.
To download the 590 KB pdf click Treadle Lathe Plans
I found the second plan on the web, also many years ago. Nowhere in this 14 page pdf is the source identified. It is clearly from an older magazine, I suspect it was an older Popular Science plan. It looks like an efficient solid construction and the heavy cast concrete flywheel should do a nice job of storing energy, to even out the power output.
To download the 14 page 389 KB pdf plan click Treadle Lathe.
I have a number of other plans for treadle type lathes. The examples I have posted are a good start, I may revisit this at a later date.
So going to take a little break here, check back end of the week for more blood pumping, excitement inducing, project plans. Insert tongue-in-cheek imoji.