If you look at page 20 of tie's schematics PDF, the left turn is indicated as "For left-turn cyclists to dismount". Obviously this manoeuvre means cyclists would have to re-mount in (potentially very busy) traffic.
Anecdotal evidence on this issue was posted on a different forum recently. Apparently CEC's requirements differed from those set out by tie's designers, and there was the intention for cyclists to be able to turn left with some sort of 'across the footway' and 'behind the pedestrian crossing' arrangement, and a caveat that the building works did not yet reflect CEC's request.
Perhaps a dropped kerb or two and some magic paint will be forthcoming. I suppose keeping the left-turn lane would just encourage motorists?
If only James Craig could have forseen buses and trams and cyclists in the year 2010. He might have built Hanover Street a few more metres to the west.