I walk through that intersection most days. What they've done in NYC is interesting. That part of First Avenue used to be, like most in mid and upper Manhattan, six (or sometimes more) undifferentiated lanes.
The first change was the addition of dedicated bus lanes (right-most lane, painted reddish), complete with violation cameras and automated ticketing. This reduced competition among buses and cars -- in favor of buses, leading to somewhat better bus throughput. Cars now had five lanes -- although with parking in at least the left-most lane, and delivery trucks double-parked adjacent to the cars, more like three.
Then came the big bike lane initiative. In the book Traffic, by Tom Vanderbilt, some of the takeaways are that parked cars can form a buffer between flowing traffic and bike lanes, and that narrowing roads at intersections through the addition of islands with trees on them increases pedestrian safety (in no small part by reducing the speed of turning cars at intersections). To varying degrees they've applied these ideas -- the left-most lane is now entirely a bike lane (painted green, complete with its own traffic signals). Next to that is a dedicated parking lane -- yes, in lane two -- often buffered by concrete islands at intersections, with a tree or two. You can see this here [1]
Cars now have three or perhaps four lanes for general travel. For left turns, the bike and parking lanes are cut by a dedicated left-turn waiting lane [2] (usually with its own left turn signal, so left turners are not fighting pedestrians in the crosswalk).
On some avenues they then added "Select Buses", which work on a "trust-but-verify" honor system so riders can enter and exit quickly through any of three wide doors without queueing to dip a Metrocard.
Finally, they cut the city-wide speed limit to 25 miles per hour, adjusting the timing of avenue traffic signals accordingly.
The result of all this has been much gnashing of teeth and rending of garments, but as a whole it's made the city substantially better for bikers and pedestrians, and in many cases left turns are much easier for drivers.
[1] https://www.google.com/maps/@40.771088,-73.9538,3a,75y,53.97...
[2] https://www.google.com/maps/@40.771088,-73.9538,3a,65.7y,194...
[Edit: clarity]