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The Meryl Streep character appears to be at least inspired by, if not actually based on, Bebe Buell. She had more-or-less simultaneous affairs with Steve Tyler and Todd Rundgren during the 1970s; when little Liv arrived she decided to nominate Todd as the dad, even though years later it turned out that Steve was the real baby's-daddy.
Apparently the script writers decided to conflate this true story with the novels "Lace" and "Lace II." (Remember the memorable lines from those classics: "Which one of you (censored) is my real (mother, father)?")
And yes, my gf's and I plan to see it.