A spokesperson for Tees, Esk and Wear Valleys NHS Foundation Trust said: “Our hearts go out to Lucy’s family and friends.
“We are looking closely at the care Lucy received from us and, in keeping with national guidance, we will establish if there is anything different we could have done to prevent Lucy’s death.
"We will support Lucy’s family through this process as their involvement is incredibly important."
A spokesperson for NHS Humber and North Yorkshire Integrated Care Board (ICB) expressed their condolences to Lucy's family and friends, and said it would "not be appropriate" to comment further while a review is under way.
The Department for Health and social care said it was "unacceptable" that anyone should feel let down by maternity support services.
“Specialist perinatal mental health services are established in all parts of England, but we know more is needed," a spokesperson said.
"Too many people with mental health issues, including mothers who have recently given birth, are not getting the support or care they need.
“That’s why we’re reforming the Mental Health Act to fix the broken system and give more people greater say over their care.”