They initially assume the correct colour is black, due to Himiko being a death queen.
It's a color puzzle.
The death queen turns the day to night...
But after this (and all subsequent colours) failing to work, Lara realises the reference is green from life, created by combining blue and yellow:
The death queen turns day to night.
She must die, to bring back life.
The color of life...
We're running out of floor!
However, since the first attested Japanese accounts of Himiko are from the 8th century, and in Old Japanese the colours 'blue' and 'green' both came under one name ao 青 (similar to how 'violet' and 'indigo' are both shades of purple in English)1, the riddle seems a bit anachronistic.
1. In modern Japanese there is a distinct word for green, midori 緑. But this word used to only refer to new buds and shoots, only recently coming to mean the colour via metonymy. Further, ao is still used in many terms to refer to 'green' items:
- aoshingou 青信号あおしんごう ("green traffic light")
- aonegi 青ネギあおねぎ ("green spring onion.")
Further still, midori itself can be ambiguous:
The word midori is also used for representing the dark blue color of the sea as a poetic or literary expression. Midori not only means onshore nature but also the sea as a source of life.
Midori also represents fresh life such as in newborn babies (みどり児, midorigo), or the shiny black hair (みどりの黒髪, midori no kurokami) of women. These are examples representing original meanings of midori.
The coloured stones:
The 'Ordeals of Himiko':
"Ordeals of Himiko"
Cross the chasm of Souls, witness the futility
Pray to [...] the 8 faces of Himiko
Manifesting the fate of her Enemies
Behold her thousand hand-Maidens, blessed
by the Ritual [S...]; Descendupon Himiko's
final Resting Place
Unleashing her Scourge
Note: the coloured stones are recovered from the mouths of 8 stone faces carved into the walls of the puzzle room.
The quote containing the riddle which solves the puzzle doesn't appear to be in the sample images below, but they may only be a subset of the pages of the actual journal prop: