Im at least 90% sure that visual stuff like light levels are calculated client-side. Thats why sometimes blocks wont be lit up properly for some people, but fine for others.
No, it is done by the server to figure out if mobs can spawn. Ever seen a monster by a lava lake with no way he could have gotten there? I have, they can spawn there before the server has updated the light level caused by the lava. How about the random dark spots under cliffs that disappear when you get close? That happens because the server didn't bother to update the light level until a player got there and until then told the client that it is zero light right next to 15 light, totally makes sense but the client doesn't argue.
Other way the server updates light levels is using block updates. And removing lava source blocks causes block updates as do the flowing blocks.