The only other three year la nina I can find besides 1998-99 through 2000-01 in this list is 1973-74 through 1975-76.
https://origin.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ONI_v5.php
I thought this was interesting too
https://www.pmel.noaa.gov/elnino/lanina-faq
Is there such a thing as "normal", aside from El Niño and La Niña?
Over the long-term record, sea-surface temperatures in the central and eastern tropical Pacific diverge from normal in a roughly bell-curve fashion, with El Niño and La Niña at the tails of the curve. Some researchers argue there are only two states, El Niño and non-El Niño, while others believe either El Niño or La Niña is always present to a greater or lesser degree. According to one expert, NCAR's Kevin Trenberth, El Niños were present 31% of the time and La Niñas 23% of the time from 1950 to 1997, leaving about 46% of the period in a neutral state.
Other notes: this seems to show that 2014-15 and 2015-16 was a two year el nino, and the only other examples of that are 1986-87 and 1987-88, 1976-77 and 1977-78 and 1957-58 and 1958-59 and 1968-69 and 1969-70. Also 2015-16 seems to be the strongest el nino on record, beating out 1997-98.