Mach 3 can control up to 6 axis of movements. (XYZ and ABC) How you build your machine, will determine the amount of control you can expect Mach 3 to handle. If I am interpreting correctly what it is that you have in mind (two routers on sleds which travel along the lathe bed) you will be somewhat limited in what you can automate. (Ideally, 3 axis of control for EACH router would be best). But since Mach 3 can only handle up to six axis, this would mean the "platter" would have to be under manual control. Or at least one axis of control would have to be manual on one of the two routers. However, if you construct a 4-axis mill table, with a lathe along one side of it, you would have all the control you should need, using only 4 axis of movements! I designed, and built a 4-axis machine. Which does pretty good, however a word of advice: invest in a photo-cell and laser type of homing switch for the 4th axis (lathe axis).
Because mechanical contact switches of any kind will beat themselves to pieces with use, and are just not very accurate in terms of consistency when homing the 4th axis to zero. This is just the machine side of things. For the "synchronized" subject, this will depend on your CAM software, and the tool paths generated by the software for use in Mach 3. Since you mentioned that you are an experienced CNC user, I am sure this is probably nothing new for you. The G code will determine what tool movements/work piece movements happen when (in order to "synchronize" things). Even though you mentioned using two routers, the reality is that a single router cutting on a work piece in the lathe jaws of a 4th axis, WHILE the 4th axis is rotating, will have plenty of work to do (which exerts quite a strain on the drive system of the 4th axis). A second router, also cutting on the same work piece, would probably be too much for the 4th axis to handle (unless of course, you construct a monstrous drive system for the 4th axis $$$$). You mentioned using Arduino, and Actuators as drive mechanisms. If you intend to place your machine under Mach 3 control, I would recommend using either stepper motors, or servo motors and lead screws (or ball screws) as the drive mechanisms. Folks tend the think that "just using a machine to cut wood" doesn't require very much torque, or power. Which is probably true, IF you are cutting Balsa wood!
But for all other types of wood, you need POWER, RIGIDITY, and ACCURACY if you want repeatable results! I used NEMA 34 stepper motors, rated at least 900 ounce inches of torque with 5/8" diameter 10 threads per inch lead screws, driven by a Gecko G540 controller. If you are truly committed to building you own machine, a word of advice: Start NOW writing your "Owner's Manual", and begin recording ALL information in the book. Design drawings, actual dimensions, parts, materials, component specifications, where they were obtained. Also any alternate suppliers. (There will come a day, when these parts wear out, and are in need of replacement- it is good information to include in the Owner's Manual for your own easy reference). Also include Part numbers for things like bearings and belts. Thread sizes, and such for every nut and bolt used to construct the machine. All materials used.
Screen captures of configuration screens for all software used (especially Mach 3). A well organized, and written Owner's Manual can be almost as much work as actually building a machine. But it is time well spent for your own reference. And can make the difference between selling your machine, or hauling it to the scrap yard, should you ever decide to part with it in the future. Good luck on your build! Have a blessed day! -Michael