I think this issue came up on another clicket and it turned out that both the right-hand lanes continue across to the south side of the Grove Street. The problem is that they don't line up (i.e. if you were to go straight from the middle lane/left-hand through lane on the north side of Grove, you would end up in the right-hand lane on the south side of Grove). As much as I dislike them, I think a dashed white line guiding the southbound State Street lanes across the Grove Street intersection may be in order.

On a bicycle, I would recommend going straight from the right-hand lane, so long as the traffic isn't backed up too far. Not that I've ever done it, seeing as how I don't have a car, but I imagine that the scariest situation here would actually be attempting to continue straight from the right hand lane in a car (which is what the earlier clicket was pointing out). At least when you are on a bicycle you can stand a chance of coexisting with the people improperly entering your lane from the left. In a car, you'd almost certainly get honked at and/or sideswiped.