What concerns the server, the request itself is not a bottleneck. I guess you have sufficient time to set up the connection, as it happens only in the beginning of the session. Therefore the protocol is not of much relevance.
But consider that HTTP is a stateless protocol and not suitable for audio streaming. There are a couple of real time streaming protocols you can choose from. All of them will work over TCP or UDP (e.g. use raw sockets), and there are plenty of implementations.
In your case, the bottleneck with latency is not the server but the network itself. The connection between an iOS device and a wireless access point (AP) eats up about 40ms if the AP is not misconfigured and connection is good. (ping your iPhone.) In total, you'd have a minimum of 80ms for the path iOS -> AP -> Server -> AP -> iOS. But it is difficult to keep that latency stable. (Typical latency of AirPlay on my local network is about 300ms.)
I think live music over iOS devices is not practicable today. Try skype between two iOS devices and look how close you can get to 50ms. I'd bet no one can do it significantly better, what concerns latency.
Update: New research result!
I have to revise my claims regarding the latency of wifi connections of the iDevice. Apparently when you first ping your device, latency will be bad. But if I ping again no later than 200ms after that, I see an average latency 2ms-3ms between AP and iDevice.
My interpretation is that if there is no communication between AP and iDevice for more than 200ms, the network adapter of the iDevice will go to a less responsive sleep mode, probably to save battery power.
So it seems, live music is within reach again... :-)
Update 2
The ping-interval required for keep alive of low latency apparently differs from device to device. The reported 200ms is for an 3rd gen. iPad. For my iPhone 4 it's more like 50ms.
While streaming audio you probably don't need to bother with this, as data is exchanged on a more frequent basis. In my own context, I have sparse communication between an iDevice and a server, but low latency is crucial. A keep alive therefore is the way to go.
Best, Peter