"Lighter" vs. "brighter"

"Light", as an adjective, can certainly mean having an abundance of light, i.e. not dark.

In your context, it is perfectly clear that you mean that turning on the lamp makes the room lighter. To that effect, the following is fine:

Having more windows, the kitchen was lighter than the living room.

Using the word "brighter" is more obvious without context because it doesn't carry the ambiguity of "lighter", that being that it can also mean "less heavy". Everyone knows that turning on a lamp doesn't reduce the weight of the room so, in your example, lighter works fine.

In summary, both are fine but if you think context is unclear then "brighter" would be more obvious.

Though sometimes they can be a little flexible, "light" here usually refers to a pale(r) colour. (It can also refer to weight, both real and felt/psychological)

"I wanted a lighter pigment, so I mixed in some more white."

(Added in edit:) "The lamp's bulb's colour in my room is too light. Do you have those golden or orange lightbulbs? I don't like white light[n] by my bed."

"I like the light cream for the walls. Anything too dark, like the ochre, will suck up all the light[n] from the lamps and windows."

We can also describe an area as "having good light[n]" (or lighting):

"This office always has good light, thanks to the south-facing skylight."

"The lighting in here is great; how many bulbs are set into this ceiling?"

By contrast, "bright" is usually use for a more vivid, but also more luminous-seeming colour (it stands out, and catches your eye) (a), or for an object which emits or reflects light (b)

a)

"The petal pink is nice for a light pink, but I want something bright. Don't you have fuschia, or hot pink?"

b)

"The lamps are/The room is much brighter now, with the new bulbs in."

"The moon is very bright tonight."

"She polished the platters until they shone mirror-bright."