In the photo, Lucy, 30, can be seen holding the little one in her arms - but some followers were quick to comment on the picture, urging the former TOWIE star not to kiss her baby on the lips.
One person commented: "Lucy please don’t kiss new baby on the lips. Google it."
But fans were quick to rush to Lucy's defence, with one responding: "If she wants to kiss HER baby, that’s her choice!"
While another said: "Pictures make a thousand memories! Leave her alone and worry about your own children!"
Others however, agreed with the fan's advice, with one adding: "It’s not ok for anyone to kiss a newborn baby on the lips, their little immune systems are so weak and if they pick up HSV1 which causes cold sores, it can be fatal to the baby."
While another added: "Better safe than sorry! Babies have died through this."
The issue of whether parents should kiss their babies on the lips is often a divisive one, due to the risk of transmission of herpes simplex virus (HSV) which can be life threatening in babies.
As the NHS explain: "Neonatal herpes is a herpes infection in a young baby. The younger the baby, the more vulnerable they are to the harmful effects of infection. It's caused by the herpes simplex virus, a highly contagious virus that can cause cold sores and genital ulcers in adults.
"Herpes can be very serious for a young baby, whose immune system will not have fully developed to fight off the virus."
Lucy shared the arrival of her daughter on 31 May, taking to Instagram to announce the news alongside a heart emoji.
Mum-of-two Lucy recently shared a number of snaps of the little one on her Stories, describing her dark locks as 'hair goals' and posting a video of older brother Roman stroking her head.
The little one is yet to have a name, with Lucy telling followers over the weekend that she and Ryan are "finding it really difficult to name her".
Lucy also revealed she had a positive birth experience, explaining it was "quite quick and so special".
Huge congratulations to Lucy, Ryan and the whole family!
Tyla has reached out to Lucy's reps for comment.