Android 5.1.1 build LMY47W for Nexus 7 (2013) and build LMY47S for Nexus 9 are indeed explicitly mentioned in a table (see image below) which summarizes the progress in lowering the audio latency in the various versions of Android.
This tells us nothing about the possible release times, but apparently it is a version so stable as to be used for public reference a table, so in theory it should be ready for the general public. We just have to wait to find out. Source : AndroidPolice