A week prior to Julian Bashir's and Jadzia Dax's meeting at Quark's, an envoy visited Deep Space 9. Dax reminded Bashir about his interest in her, but Bashir answered that she was a barely adequate substitute for Dax. (DS9: "If Wishes Were Horses")
This woman refused to wear a wig with a small animal in a cage inside, a fashion which had become tradition among Betazoid women by that point. Her defiance was responsible for changing the custom. When Lwaxana Troi told Timicin about her in 2367 – in an attempt to convince him he should defy Kaelon tradition and refuse to commit ritual suicide – he remarked that this woman must have been a lot like Lwaxana. (TNG: "Half a Life")
There were several members of Lwaxana Troi's family, including her parents and a sister, who had all died prior to 2372. That year, she confessed to Odo that the loss of her family, as well as her husband Ian Andrew Troi and especially the loss of her daughter Kestra had made her depressed. (DS9: "The Muse")
Lwaxana's father, who was Deanna Troi's grandfather, was someone that Troi spent time with on Betazed while growing up. He was a man who rarely spoke, noting that talking was for off-worlders and people who didn't know any better.
When Troi got older, the only time that she could remember his stories was when she went home to Betazed and sat by the fireplace, adding that at times, when she was alone there, it was almost like she could hear his voice inside her head. (TNG: "Eye of the Beholder")