I have no idea.... but;
have a look at Lance Warrens site 3ROTOR.COM
there is a truckload of info there and in the links about the JC Cosmo.
It's a Japanese domestic model, ie not for export, so its a RHD set up out of the box... and most likely only came out RHD. Possibly a model was made for testing in the US... but if such a beast existed, it has likely been destroyed or returned.
If an RHD to LHD is as hard as an LHD to RHD... then it can be done, but will be difficult - you will need to redesign the entire interior set-up, moving dash etc, altering all wiring... etc. Making it look good would be the easy part! These cars are loaded with options, climate control etc, so that needs to be re-jigged. THen there is the steering.... yikes, the firewall will need complete revision, clutch , brakes etc moved, hard-lines re-routed, the floor pan shape might not be conducive to having a driver over there ( ... arrgh!) Who know what the problems could be. Unless money was no object.... then you would have to be very skilled to do it in a cost effective way.
Meeting US emissions and registration regulations could be fun! It is a challenge to make it meet australian ones!
THere is a bright yellow one in Sydney, Australia - there might be pics for it it off the Pac Performance web site. Rego plate is something like Mrs20B... In a bright colour it looks very different!