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Dozens of tributes for Ms Lovell, who is survived by her husband Nick and daughters Lulu and Zahra, have been posted online.
"You taught us how to love. Always in our hearts," one read.
Premier Ted Baillieu indicated a ban on home birth was unlikely.
"I don’t think we should ever, in any circumstances, rush to judgment based on a single experience,” Mr Baillieu said.
“Obviously some people choose to home-birth, the vast majority of people go through a birth process at a hospital.
“I don’t want to make any judgment about this particular case.”
Ms Lovell, who was a professional photographer, was described as "a healer and friend to many more".
A spokeswoman for Midwives in Private Practice said it was the first time she has heard of a maternal death following a home birth in her 15 years' experience working as a midwife.
"It's very very rare and it's just impossible to imagine what might have happened," she said.
Source: Herald Sun