Start with 0-walls and walls that already have their full lamp count. Then check each unlit cell's open row and column. If only one place can light it, that place needs a lamp.
A wall marked 0 cannot share an edge with a lamp. Marking those cells empty makes the next lamp choices easier to see.
Before: several 0-walls still have unmarked neighbors, so too many cells still look like they could hold a lamp.
After: every neighbor of a 0 has a purple X, which means no lamp can go there. These cells still need light from somewhere else.
Turn lamp rules into exclusions
Close a satisfied wallIf a wall already touches its full lamp count, mark all remaining white neighbors as unable to hold a lamp.Fill the remaining spacesIf a wall needs two more lamps and has only two possible neighbors left, both neighbors must hold lamps.Clear the lamp's row and columnA placed lamp rules out all other white cells it can see in the same row and column, up to the first wall.Find the only light sourceFor an unlit cell, check every possible lamp place in its open row and column. If only one remains, put a lamp there.
Stop each sight line at a wall
A lamp lights through white cells only. The first wall stops its light, even when that wall has no number. A cell beyond the wall may still need a different lamp.