Lila Cole, also known as Lylita Vataix, was a wealthy Betazoid scientist and ambassador residing on Brekka. Cole specialized in archaeology and specific philosophical topics related to specific Brekkian cultures.
Cole was a daughter to the Eleventh House of Betazed before giving up the Vataix family name following disputes with her family, whom last saw her when she left for the Delos system in 2360. She is met by Rex Blake upon arrival, and after two years of courtship, the two have a daughter - Sky Blake. Cole's relationship with her daughter becomes strained when she leaves the 'safety' of Brekka for Starfleet upon a fellow Betazoid's recommendation. After twenty years of marriage, she suddenly divorces Rex, and lives in solitude within Seritonia, Brekka. Rex is presumed deceased during a domestic terrorist attack in Lornae during mid-2389.
She remains on Brekka until her daughter returns, and takes custody of Blake's children Faith and Ayden when Blake disappears. It should be noted that, despite the exaggeration of Blake's death, Cole requested her daughters records removed from the Starfleet database upon perceived confirmation. When Cole tells Blake she will look after her children no longer, they are relocated to Ornara, and mother and daughter never speak again. It's presumed they were never on amicable terms, nor do they attempt to reconcile.
Cole's death is recorded as having occurred on stardate 239410.12, and word reaches her daughter over two months later through the Vataix family, whom wished to reconnect with their lost cousin. However, the nature of her death is not explained.