A high-density 5 1/4" floppy can be modified to work in a Twiggy drive, that is true, because the actual magnetic media donut inside the envelope is essentially the same as that used by the Twiggy. (IE, it coating is of similar magnetic coercivity, higher than that used by the media in standard-of-the-time double density disks.) Because the envelope dimensions are also the same the conversion process in principle involves not a lot more than cutting a second set of access windows mirror-imaged to the stock one (after removing the donut through an open seam, obviously). Compared to a normal floppy disk the holes in a twiggy disk are rotated 90 degrees compared to a normal floppy; IE normal:
Twiggy:
Notice that the Twiggy disk has an index hole in it which I don't think they actually used. It kind of implies to me that the disk manufacturers actually turned out the twiggy disks using the same plastic blanks used for normal disks, they just punched some extra holes in them after they'd already gone through the die that cut the standard holes.
As to recreating the actual drive, good luck with that. As the holes demonstrate the Twiggy used a completely nonstandard arrangement for writing to both sides of the disk, IE, instead of having the two heads oppose each other like a normal double-sided drive they had each head opposed by a fiber "shoe" like you'll find in a single-sided drive and had the back side read by a complete duplicate mechanism. The two head-read mechanisms rode a single positioning screw, so as the head on one side moved inward from the edge to the hub the opposite head moved from hub to edge. Because the Twiggy *also* used a variable speed motor to pack more sectors into the outer rim than closer to the hub this means the "proper" way to read/format a twiggy is to advance all the way through one side of the disk, edge to hub, with the motor speeding up along the way so to maintain the near constant linear velocity required, and then slow down the motor and go back the other way with the opposite side's head. This is exactly the opposite of what you want to do with the 3 1/2" variable speed drive in the Mac/later Lisa, where it's more efficient to read-write both sides on a given cylinder before stepping the head. Therefore there's no way to take a normal 5 1/4" mechanism with opposed heads and make it "emulate" the Lisa drive, you'd *have* to change the software driver.
If you're talking going all out and making new Lisa mechanisms, well, sure, you can do that. Start by disassembling two standard floppy drives for parts, then get yourself a lathe and CNC router to build a new frame, positioning mechanism, etc. Might be an interesting hobby. Just keep in mind that the Twiggy failed because it was actually a terribly flawed device both in principle and in execution: Apple wasted millions of dollars trying to make it work and ended up writing it all off in the end. I kind of doubt a DIY one will work a lot better.
I just wish that someone out there makes replicas of these old machines (especially the rare ones). If an Apple-1 replica exists, then I think that a replica Lisa 1/2/XL should exist (even though it is more complex and harder to recreate). Having these machines and prototypes (Macintosh Twiggy) not only available to serious collectors, but also average ones would make me so happy to see. 
