Well- it works like this. Your lawn tractor was designed to run at a maximum ground speed of maybe 7 or 8 mph, max. As such, none of the componentry is really up to the task or performing at 30 MPH. The frame is flexy, the front axle beam pivots, the brakes are less than impressive, the rod ends are inadequate, and the bearings are crap (if it even has bearings- most use bushings). The alignment is poor, the geometry is less than wonderful, and there's slop where there shouldn't be.
In short- yes- you can attain that kind of speed. Should you do it without addressing all the other, related issues? Probably not.
I have started a racing mower project, myself. I am modifying the wee out of it and have a pretty good feel for what's involved. Not gonna be much left of the original machine, that's for sure.