Somehow it seems to be connected with Lift Off sensor or Synapse.
First, I have updated firmware and up-to-date Synapse 3. Everything was working fine, till today.
When I set Basilisk's LIGHTING OFF in Synapse, it stays off, just how it should, but when I lift my mouse up (so the sensor has no connection with any surface) then LEDs on mouse turns and stays on (in Synapse it is OFF). When I put the mouse back on a mousepad (or cover sensor with my finger) then mouse lighting comes off. Lift it up again (or uncover sensor with a finger) and lights come on again.
THIS ISSUE:
I found out that it only occurs, when in wireless mode (doesn't matter if USB dongle is in charging dock, or directly in PC's USB port). When wired, everything is fine.
Also, when I turn OFF and back ON the mouse (resetting by switching on/off at the bottom) the issue is gone, until the moment I switch the lighting on in Synapse and then back off.