How does this serial input DAC work?
The converter needs one 16 bit word for both channels, L first and then R. LRCK shows to the converter is there coming in data for L or R. Both words come in MSB first, LSB last.

The output of the converter is made from the last fully inputted L+R word pair. The output changes when the input of the next L+R word pair is started. Both channel outputs change at the same time, because people generally do not want any time delay between L and R signals, the timing must be "sample accurate".