Synchronization and audio stream latency, lag with Webradio sound

Real-time transmission doesn't exist. It is never instantaneous due to the wide variety of parties involved, the need for buffers and restrictions inherent to each stage. An approximate 3-4 seconds latency following the moment the sound is generated is perfectly normal.

There is always latency since, if nothing else, the player takes at least 1 to 2 seconds to preload the buffer before starting playback. By default, Icecast has a 64KB buffer, roughly corresponding to 4 seconds of broadcast in 128k MP3.

Encoding clients generally have buffers which allow to minimize blanks. There exists several latency points, corresponding to the various buffers used. It's possible to reduce the buffer in order to reduce latency, however it is risky, for Internet connections cannot guarantee constant and stable bandwidth. Latency is your enemy, buffer-size your ally. Play around with the size to maximise your broadcasts.