Not only are you allowed to.....
Hey, all you cagers (and motor-heads on two wheels as well, for that matter)!
Not only are you allowed to (safely) enter the bicycle lane to effect a left-hand-turn, you are *expected* to. It is NOT the intent that you make your turn from an inner lane CROSSING the bicycle lane (very dangerous and presumptuous). Turned around and looked at from another angle, if you can't safely get to the curb *before* making that turn.......
wait for it........
THEN YOU CAN'T MAKE THAT TURN!
If you left it too late and there are a bunch of bicycles on the outside, well too bad, so sad, move on (in a straight line, and go fix your screwup on *your* time without making it everybody else's problem).