@Bats on mine (PM-1228) the manual specifically states that you can switch from forward to reverse without pausing or powering down. The digital controller brings it to a stop and then ramps it up to the set speed. Headstock is D1-4 as well. But yeah - "refer to your owners manual". This might be a special feature of my machine - I don't really know.
I've never used a D1-4 (all of my lathes have simple threaded spindles), but if I understand them properly, yeah, they'd be perfectly happy with a quick reverse. A little more digging says that the Grizzly has an "intrinsic backplate" spindle - which sounds like a flange that the chuck bolts to. I imagine that would also be ok with reversing, but it would may be hard to find alternative chucks for it (4-jaw, collet, etc), and definitely sounds like it'd be a pain in the ass to swap them.
edit: Now that I look at the LMS table, it sounds like all the 7" models work the same way, so my arguments should probably be ignored like the uninformed tripe they are.
I haven't looked into whether the switch can be changed on the fly, but it looks like you probably would want to stop the machine when changing the gears or they'd probably explode (the gears that is, I think they're plastic unless upgraded).
Yeah, you'd definitely want to stop before throwing the tumble gears. On my South Bend Light 10 (all cast iron and steel) it's
possible to flip them with the spindle running, if you get it
just right... but usually it grinds the gears and makes terrible noises and tells you that it'll spit teeth in your face if you ever try a stupid move like that again, moron.
My understanding is that most metal lathe chucks are good for forward/reverse, unlike most/many wood lathe chucks, but again "refer to your owners manual".
It very much depends from one to another - the old South Bends and I think most of their derivatives (Logan, Hercus, maybe Myford, etc) used threaded spindles. It sounds like most of the 7" models are bolt-on. When you start getting into bigger modern lathes, things like the D1-4 become more common. So, yeah, "refer to your owner's manual", get to know your machine, and then use your common sense to fill in the blanks. If you don't have any, borrow someone else's common sense. Preferably someone who knows something about machine tools.