Sorry I can't help with info on the Lyman but I can with the Lee.
I currently run 2 presses, a Dillon XL650 for loading .45acp and the Lee I use for 9mm.
Yes, I do realize that I can use one press for everything but when I started reloading I started with the Dillon.
Along the way I realized that I enjoyed the process of reloading and I purchased the Lee both as a comparison and to slow me down a bit as the Dillon loads ammo very fast.
I cannot say that I had any problem with the Lee though I only had it a short time. The only reason I got rid of the Lee was expense, I was loading so much ammo on the Dillon that it started to cost a bit for components and I couldn't afford to keep feeding both machines.
My solution was simple, I kept the Dillon for the .45, sold the Lee and bought a Lee Classic single stage for the 9mm.
I now have the best of both world, I can load ammo in high volume on the Dillon while still enjoying the hobby of reloading which I happen to enjoy almost as much as actually shooting.
I have had no problem with either Lee.
You want a Ferrari get the Dillon and if a Chevy Cobalt is ok with you then get the Lee. They both do the job and even a Chevy Cobalt can be fun.