DIAGNOSIS Audio delay from digital audio processing, common when using an AVR, soundbar, or TV in 'Game Mode' or with specific audio formats.
FIX Manually adjust the audio sync. Go to Settings > Display & Sound > Audio > Audio delay. While playing content, use the plus/minus buttons to adjust until the audio matches the lip movement.
IF THAT DIDN'T WORK Change the audio format being sent. Go to Settings > Display & Sound > Audio > Surround sound. Try setting it to 'Never' or 'Manual' and select a simpler format like 'Stereo'. This reduces processing delay.
HEADS UP If you use an HDMI input on a soundbar first, then pass video to the TV, the soundbar may be causing the delay. Bypass it and connect the Chromecast directly to the TV to test.