What color pattern opens the lamp compartment in Level 54?

Leave the top lamp white. Set the lower lamps blue on the left, cyan in the middle, and pink-red on the right.

Where does the Level 54 key come from?

Put the loose cog into the empty gear-chain slot and rotate the marked wheels into one meshed chain; the mechanism drops the key.

The Vault: Logic Puzzle Box level guide

expert 8 colors

Release the screwdriver, set the white-blue-cyan-pink lamps, align the colored disc, mesh the cog chain, and open the pipe hub.

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Open the scrollwork shutter on the pipe face, collect the red-handled screwdriver, and use it on the side housing to take the loose cog.
Move the red rail beneath the four fan gauges until their hands match, then set the triangular lights to top white, lower-left blue, lower-middle cyan, and lower-right pink-red.
Take the handle from the opened lamp flap and rotate the six-sector disc until blue, cyan, yellow, white, orange, and red sit under their matching colored rim pins.
Use the released curved handle on the low latch, place the cog in the vertical gear-chain gap, and rotate the gears so the large top wheel meshes through the small middle wheels to the lower marked wheels.
Copy the gear glyph arrangement onto the four three-high symbol reels: hooked angular/oval/stepped angular/diamond-eye across the top, hooked/inverted triangle/X/diamond-eye in the middle, and crossed-bar/flat hook/hexagonal arrow/oval at the bottom.
Use the dropped key in the brass lockbox, turn the three pipe arms until they join at the hub, and open the iris around the Respiration Coral portal.

Colors in this level:

Brass, White, Blue, Cyan, Pink, Red, Yellow, Orange

Match each disc sector to its same-colored rim pin, not to the neighboring sector.
Seat the loose cog before rotating the marked gears; the chain cannot issue the key while that gap is empty.
Keep the triangle orientation fixed when comparing the lamp face, disc, and gear face.

Board notes 5 details

Layout: A weathered brass triangular box has a scrollwork shutter over three pipes, four upper fan gauges, a triangular lamp cluster, a six-color disc, a vertical gear chain, and a low lockbox.
Goal: Use the color and gear clues to obtain the key, then lock the three pipe arms into one central hub and open the triangular iris.
Opening: Open the scrollwork shutter for the red-handled screwdriver, use it on the gear housing, and keep the released cog for the only gap in the gear chain.
Danger Zone: The lamp solution is triangular: the top lamp stays white while the lower row is blue, cyan, pink-red from left to right.
Mechanics: Gauge positions activate the lamp colors; the color-disc pins release the handle, and the meshed gear glyphs become the final symbol-reel configuration.

What color pattern opens the lamp compartment in Level 54?
Leave the top lamp white. Set the lower lamps blue on the left, cyan in the middle, and pink-red on the right.
Where does the Level 54 key come from?
Put the loose cog into the empty gear-chain slot and rotate the marked wheels into one meshed chain; the mechanism drops the key.