I guess, I have managed to get it working.
Found this post
lxc config device add <container> pcmC0D2c unix-char path=/dev/snd/pcmC0D2c
I have added all devices listed in /dev/snd:
controlC0 hwC0D0 hwC0D2 pcmC0D0c pcmC0D0p pcmC0D10p pcmC0D1p pcmC0D2c pcmC0D3p pcmC0D7p pcmC0D8p pcmC0D9p seq timer
It is important to add seq and timer, as well.