LGBT activists had advocated for a law like this since the country legalized same-sex marriage in 2013.
The Italian system does not offer artificial insemination to lesbian parents and registering a child may require the mother to lie that she had sex with a man.
The lawsuit claims the Idaho Falls reproductive specialist told the couple he would use the husband's sperm mixed with a donor's sperm, but instead used his own.
The procedure allows mothers to avoid passing serious genetic conditions to their children.
Due to an error, 26 women's eggs may have been fertilized by sperm from someone who isn't the "intended father."
The World Health Organization said infertility should not be regarded as simply a medical condition.
Experts have called results of the world-first study "remarkable."