I can answer this one!!!
I've called Tikka Finland, Stoeger Canada (Canada's Tikka importer), even Beretta New Zealand. The Tikka CTR does not and will not, at least in the near future, exist in Left-Handed.
Other Tikka's can be had in left handed and .308.
If you want the set trigger and LH, all that's in Stoeger Canada's catalogue are the following:
T3 SPORTER HB LEFT HAND LAM/BLUED 223 REM NS W/SET TRIGG, MT
T3 SPORTER HB LEFT HAND LAM/BLUED 260 REM NS W/SET TRIGG, MT
T3 SPORTER HB LEFT HAND LAM/BLUED 308 WIN NS W/SET TRIGG, MT
T3 SPORTER HB LEFT HAND LAM/BLUED 6.5X55 NS W/SET TRIGG, MT
That said, the Sporter HB is pretty badass.