I am a lefty and love my UDT for daily chores. I pondered the same question too. First I took the clip of, attached the lanyard and carried as a pocket knife, in the left pocket of course. However, now I like to carry it clipped in my left back pocket. That way, the spine of the blade rests against the seam of the pocket. This way it provides me with more of a feeling of security, should it accidentally open. I even tried carrying it IWB on the left side of course, but I felt it was too 'complicated', but that's personal. I definitely suggest using the lanyard on the UDT, it greatly aids in getting a fast and easy solid left-hand grip on the knife.
Too bad MT doesn't offer more lefty models. Apart from maybe Sebenza's, there aren't too many higher end lefty utility folders, but I find the UDT to be an excellent alternative.
Wouter