Not having played Lorcana, but reading about what different inks represent, there seems to be some overlap with Magic: The Gathering colours.
Amber ink represents community, patience, and loyalty. It has bodyguards and healers which are both defensive in nature. This quite closely resembles the color white.
Amethyst ink represents characters with magical abilities. It has powerful effects and hand manipulation. This feels very much like Dimir (blue + black).
Emerald ink represents flexibility and control. It can return characters to opponents' hands and force them to discard. This also feels very Dimir.
Ruby ink is aggressive and reckless. It has rush, which is equivalent to haste. This is clearly synonymous to the colour red.
Sapphire ink is about intelligence and creativity. This seems quite like the color blue, but possibly a blend with red (Izzet). It also interacts with items (artifacts?) and can search the deck (primarily black)
Steel ink is strong and defensive. It can also deal damage directly. Maybe steel is Boros (red and white)?
You'll notice green doesn't seem to match any Lorcana inks (by my analysis at least). This might be explained by Lorcana's lack of specific land cards, which are tied to green. I'm not sure if any Lorcana cards exist that manipulate your ink well, but those may be green. Amber or steel also show hints of green.