The Live is from the supply, and is live regardless of switch position (and alternates between plus and minus 330 Volts or so, 50 times a second and averaged over time has a heating power equivalent to about 230 or 240 volts DC. That is the significance of the 230V RMS rating.)
Neutral is the other terminal of the generator, and stays at around zero volts, being earthed at the substation transformer, and possibly other places too, but let's not worry about that just yet. So on negative half cycles electrons are rushing out of the live towards either gound or neutral, we prefer neutral, as if they go by any other route, something has likely gone wrong. On the positive cyycles they try and get back. So you may think of the live as alternately sucking and blowing to make the the electrons trot back and forth in the wire.
Now both adding and removing electrons hurt just as much, only the direction (current sense) has been reversed, but both an entry and an exit burn hurt equally, so us being earthed and touching live is a bad thing.
The switched live is connected to live when the switch is in the on position (or part-time connected if the dimmer is half way up the brightness scale -dimmers slice up te waveform, but the eye, and the heating/cooling inertia of the filaments conspire to smooth over the flicker.)
If the switch is off the switched live wire, the one from switch out to the lamp is dead (isolated from live), and no current flows.
Neutral, at least in this circuit, does not come to the switch at all, but goes straight to the light fitting by route as yet unknown. If swapping the wires does not move the flicker from one lamp to the other, then working out how the neutral wiring gets to the lamp (or rather how the current gets back from the lamps non-live side to the supply neutral, to keep the picture simple) is your next task, though removing the light fitting and having a look behind it is always a good start.
Flickers often mean loose screws or dirty or corroded wire not making a good shiny metal to metal contact with good contact force. Often just to dismantle clean, polish and refit is enough to restore operation, if you can find which is the poor joint.