Lily, Liina and Leila Luik are sisters from Estonia who could be the first set of identical triplets to compete in the Olympics
The record for the most siblings in the same Olympic Games is 4. This happened when the four brothers Luis Adrián, Jorge, José and Roberto Tamés from Mexico competed as two 2-man bobsleigh teams at the 1988 Calgary Winter Games. See 1 (1a), 2, 3.
Three siblings competing in one Olympic Games has happened several times:
Summer Olympics, 3 siblings
- Americans Edward, Richard and William Tritschler competed in gymnastics at 1904 Saint Louis Olympic Games.
- Japanese brothers Kazuhito and Yusuke Tanaka won silver medal in London 2012 as a member of Japanese gymnastics team. They also competed in individual competition. Their sister Rie Tanaka competed at the same olympics in both team and individual
- Steven, Mark, and Diana López represented USA at several Olympic Games. In 2008 Beijing all three of them won a medal. See also: 1 (1a), 2. 3 (3a)
- The Estonian triplets Lily, Leila and Liina Luik competed in marathon at 2016 Rio Olympics. (They were mentioned already in the question.)
Winter Olympics, 3 siblings
- The sisters Thérèse, Anne-Marie and Marguerite Leduc competed in women’s slalom at 1960 Squaw Valley.
- The brothers Marcos Luis, Martín Tomás, Matías José Jerman from Argentina competed in cross-country skiing in 1976 Innsbruck.
- The brothers Peter,
Marián and Anton Štastný played for Czechoslovakia in 1980 Lake Placid. Czechoslovakia ended up 5th in the tournament.
- In 2014 Sochi the Canadians Justine and Chloé Dufour-Lapointe won gold and silver medals in
women’s moguls, while the third sister Maxime finished twelve.
- The sisters Aita, Selina And Elisa Gasparin competed in biathlon in 2014 Sochi and 2018 Pchyongyang. Selina Gasparin won silver medal in Sochi.
- Monika, Nina and Isabel Waidacher played ice hockey for Switzerland in 2018 Pchyongyang.
- In 2018 Pchyongyang, Madeleine Dupont and Denise Dupont were a part of bronze Danish curling team. Their brother Oliver Dupont was in the men’s team.
- Multiple Siblings at the Winter Olympics (Internet Archive)
- Olympic Siblings Make Competition a Family Affair (Internet Archive)