Nicoll said the triplets, who were actually due today, have put on weight and are doing well.
They weighed between 720g and 795g at birth. Molly and Joshua now weigh over 3kg and Cameron is 2.57kg after battling a series of health setbacks.
Starship lactation consultant Lynley Nichols described Nicoll's efforts as "the Commonwealth Games of breastfeeding".
"These babies are alive because of the breastmilk and motherly care Lucy is giving her babies," she said.
World Breastfeeding Week will be marked by New Zealand women gathering to feed their babies at malls, cafes and marae for the Big Latch On.
For details of your nearest Big Latch On, 1 and 2 August go to www.biglatchon.org.nz; www.facebook.com/biglatchonNZ