-No experience with Race Deck but I had a look at their website. Only saw the open patterns, don't know if there's others that are of a closed geometry pattern. My first thought was "What a great way to trap machining chips". Yes many of the chips can be sucked up with a vacuum cleaner but chips often cling tenaciously to/under anything they can. A few places I've worked had fatigue mats similar to these and the only way to clean up after machining was to pick up the entire mat with an overhead crane and knock all the chips/curls loose for sweeping. You never get all of them either as the sharp edges embed into the rubber/plastic matrix so you just did the best you could and left what remained.
-Could these support a lathe? That depends upon the footprint area of the feet themselves. Obviously the larger the footprint the less imprinting. Will the mats allow for rolling? I suppose so but wouldn't expect a firm answer from anybody but sales to tell you so, liability makes everybody but sales a bit reluctant to commit to an answer. Ease of rolling also depends on the caster but I wouldn't feel comfortable with it until after I'd done it a few times. I use feedback from the casters when I roll on concrete and the odd surface would be a new learning curve. Almost all lathes are decidedly top heavy and I need all the feedback I can get to tell me when something hangs up a caster from rolling (like chips) so I don't keep shoving, it doesn't take much effort to push a top heavy machine over or lose a caster that's not bolted on. If the mats separate and leave a gap I can imagine the caster falling into the gap and cause a heart stopping disaster. Maybe I have an over-active imagination or too many similar experiences on the job.
-Would I advise using these mats? Can't speak for or against them. They seem nice but for reasons I've mentioned I wouldn't use them around machinery until my questions were answered and/or I tested them. They seem nice but that's probably a large, expensive chance. That's just my personal opinion. If you get them do report back, I'd like to know how they worked out over time.