The basic process is not much different from RHD -> LHD Elise conversions and there should be various websites on the net documenting those. Conversions on Toyota based Elises should be the closest match as esp. the later ones share bits like ABS system, similar pedal box, etc.
A lot of it is in the 'lots of work' category but not difficult once you strip the car down to mostly the bare front end of the chassis and empty out the passenger compartiment of all parts and then start swapping bits over from one side to the other like the pedal box, wiring loom routing, etc.
Some of it is not 'side specific, other bits are..
It also depends on how clean/neat you want to do the conversion. You can choose to leave the ABS modulator and electronics on the 'other side' of the car. This will mean getting the battery in and out will become virtually impossible though unless you go to a race battery. Moving it over to the 'correct' side will make it more 'original' looking, but will mean buying the (identical) LHD upper suspension mounts from an LHD Toyota Elise and re-making a bunch of brake-lines. (good idea anyway as linkely some of the original steel ones will be corroding)
The issue you will be mainly running into is obtaining the parts that are specific to LHD vs. RHD as pretty much all VX/Speedster specific OEM parts from GM that are not shared with the Elise are no longer available new. They sold off all their parts supply a few years ago so you'll have to rely on Ebay and the like or (some) reproduction parts.
You will also need to (re)fabricate parts or modify them to suit. Eg. the passenger compartiment is not specifically LHD or RHD in itself, BUT the components are not mounted symmetrically (drivers seat is fitted more to the center) and this means that for instance the plastic gear lever cover IS somewhat a-symmetric and won't fit right when swapped to LHD unless you modify it.
Big stuff like the dash top (also no longer available) are fairly obvious parts needing modifications.
As a lot of parts are shared with the Elise, it's a good idea to get the Elise service manual and examine the VX/Speedster specific info on here: https://www.speedste.../epc/index.html https://www.speedste.../tis/index.html
Take your time and slowly work through it. On the 'other side of the pond' you'll be hampered even more by lack of parts availability (apart from the engine), so I'd expect it to take quite a while.
Bye, Arno.