Twins competing in the same event is not uncommon at the Olympic level. But the Luiks are believed to be the first identical triplets to compete against each other.
The blond, blue-eyed sisters from the southern Estonian university town of Tartu, now 30 years old, only took up serious distance running when they were 24.
"We have been active since childhood, we love dancing, we love to be active and this pushed us to professional sports," Lily said.
The Rio Trio set to make Olympic historyPlay! 01:39
Liina, who got the sisters to start running, said long-distance running appealed to them more than the highly technical nature of sprinting.
After a couple of years, they realised they were good enough to take part in international competitions. They decided to try for the Olympics, adopting the slogan "Trio to Rio" to give shape to their hopes of all three competing in the Olympics.
"We saw ... after one year we had good results in Estonia and we thought we could achieve something good also outside of Estonia and to do some big competitions like European Championships and the Olympic games," Lily said.
In competition, the sisters say they support each other emotionally and even in race tactics, such as taking it in turns to act as wind breakers.
The sisters live separately in Estonia and sometimes have to train apart. But they regularly spend winters together at a high-altitude training camp in Kenya, and they appear to enjoy each other's company, chatting away while running. They will all be training in northern Italy from June for Rio.
"It is boring to train alone," said Leila.
The sisters are not favoured to end up on the podium at Rio. Ethiopian superstar Tiki Gelana set the Olympic record of 2 hours, 23 minutes and 7 seconds in London in 2012. The silver and bronze medal times were 2:23:12 and 2:23:29.
By contrast, Leila, the oldest of the triplets, has the fastest personal best at 2:37.12, set in Shanghai in 2013. She is followed by Liina, whose personal best is 2 minutes and 30 seconds slower and Lily, the youngest, who is a further 45 seconds back.
But all three said their goal for the Rio games was to finish together, to set personal bests and to finish with a smile. Asked if they expected to bring home an Olympic medal, all three chimed in.
"It would be great ... it's like our dream, and we know that we have to live in reality. It is very hard to compete against the Kenyan runners. We are not at the same kind of level as they are now, but in two or three years we can do that."
And while they may be identical in appearance, their running style does differ.
"If all three of them run together, I can easily tell them apart," said Harry Lemberg, their coach from the beginning.