For those not familiar with the area, perhaps I can shed a little light. This is a really horrible intersection which is timed in favor of Delancy (which leads to one of the free bridges out of Manhattan about 6 blocks away so it's always a mess). It is also one of the few on this street so close to the bridge that are not routinely manned by Traffic Agents (the blocks to the east and west of this intersection are). As a result, you get a ton of people who want to make this turn, thus the "dotted line" was painted to help idiots not run into each other.
But what happens is the line to turn left from Chrystie ends up going back for blocks and blocks and blocks (and even longer during rush hour) because only a handful of cars can make the turn before the light changes.
So, and I am not accusing the OP of this, you get a solid number of a-holes who think they don't have to follow the same rules as everyone else and zoom up the right lane and jump in in front of the cars patiently waiting in the left lane to turn left.
And since a photo is worth like, 14 words or something, you can see the non-rush hour line of cars here:
https://maps.google.com/maps?q=chrystie+st+and+delancey+st+ny&hl=en&ll=40.720195,-73.992791&spn=0.001789,0.004128&sll=40.719969,-73.992907&sspn=0.001797,0.004128&gl=us&hnear=Delancey+St+&+Chrystie+St,+New+York,+10002&t=m&z=19&layer=c&cbll=40.720094,-73.992843&panoid=TPt1gqdYzMs5UggF076Ivg&cbp=13,4.66,,0,5.56
And if you spin 180 from that view, you can also see this horribly "confusing" intersection.