Lāsma Avotiņa married Estonian speed skater Toivo Kauniste in 1962 and they settled in Riga. She competed on 1,000 m, 1,500 m and 3,000 m at the 1968 Winter Olympics with the best result of fifth place on 1,500 m. Kauniste is still active in speed skating, participating in Masters events.
Competing for the Soviet Union as Lāsma Kauniste, she won bronze at the Soviet Allround Championships in 1967 and silver at the World Allround Championships. Although she never won the Soviet Allround Championships, she did become World Allround Champion in 1969. She became World Champion Masters in the category over 60 in both 2002 and 2004. At the 2007 World Championships Masters, she won silver in the category over 60. Her achievements earned her the Honoured Master of Sports of the Union of the Soviet Socialist Republics title. An overview of medals won by Kauniste at important championships she participated in, listing the years in which she won each:.
