Her father Philip Bromwell, a journalist for Ireland's RTE website, took to Twitter to share Ardern's letter.
The letter, which is signed by Ardern, reads: "Thank you so much for your letter. I'm so sorry it has taken a while to get back to you, it's been a busy few months unfortunately.
"I appreciate you taking the time to write – your kind words meant a lot and they really brightened up my day.
"I hope you and your family are staying safe in Ireland, please pass on my best wishes to them."
It was also personally signed with a pen, with the PM adding "thanks again, Lily!".
Bromwell said Lily was "delighted" at the reply.
"During the first lockdown last spring, our then 11-year-old had to write a letter to a leader for school. She chose Jacinda Ardern.
"Well, after 'a busy few months' (!) for the NZ PM, Lily was delighted to get a personal reply! Great at leading, lockdowns & letters."
Irish media has picked up the story, and locals have taken to social media to share their love for the response.
"Fantastic leader. And well done to your then 11yr old getting in touch with her. They couldn't have picked a more inspiring leader in these unprecedented times," one wrote.
Another added: 'That's so cool. Lily and Jacinda are obviously both legends. Lovely by the NZ PM."
It's not the first time Ardern has replied to international mail.
A 14-year-old student from Southern India was surprised and elated to get a "beautiful and personal reply" to a letter she sent to Ardern.
Amana Ashraf wrote to Ardern in 2019 to convey her admiration to the Prime Minister, praising her for defeating "hate with love".
In Ashraf's letter, she asked after the Prime Minister's daughter, Neve.
Ardern wrote back saying that Neve was very well.
"She's growing up so quickly. It's amazing to hear her start to speak [she now says 'hi' to everyone she sees!]."
In her reply, Ardern thanked Ashraf for her words of encouragement and said her expression of solidarity had helped New Zealand.
"Knowing that we have friends around the world, who are prepared to stand with us to spread love and solidarity rather than hatred and division, has given us strength," Ardern is quoted as saying.