Amram was born and raised in Portland, Oregon, and is Jewish. She was educated at Catlin Gabel School and Harvard University where she graduated in 2010. While at Harvard, Amram wrote two of the Hasty Pudding Theatricals’ comedy drag shows with her roommate and writing partner Alexandra Petri. She studied violin for twenty years, and appeared as a violinist in an October 2018 episode of The Good Place, a sitcom on which she was a staff writer.

Previously, Amram was a writer on the Amazon series Transparent, HBO’s Silicon Valley, and the final three seasons of the NBC comedy Parks and Recreation. Her other past credits include writing for Adult Swim’s Childrens Hospital, Fox’s The Simpsons, Comedy Central’s Kroll Show, the 83rd and 90th Academy Awards, the 2012 MTV Movie Awards, the Disney Channel and contributing to Funny Or Die and the Comedy Central Roasts. Her writing has appeared in The New Yorker, McSweeney’s, Vulture, Vice Magazine and The Awl, among others, and her first book Science… For Her! was published in November 2015 by Simon & Schuster.

In 2018, Amram created, directed, wrote, and starred in the comedy web series, An Emmy for Megan, which depicts Amram’s quest to win an Emmy Award by meeting the minimum standards to qualify for an Emmy nomination in the Outstanding Actress in a Short Form Comedy or Drama Series category. The first series was nominated for two Emmy Awards, one in the Outstanding Actress in a Short Form Comedy or Drama Series category and one in the Outstanding Actress in a Short Form Comedy or Drama Series category for Amram. The second series was released in May 2019 and was nominated for two Emmy Awards, one in the Outstanding Actress in a Short Form Comedy or Drama Series category and one in the Outstanding Actor in a Short Form Comedy or Drama Series category for Patton Oswalt.

Along with her work as a writer, Amram has occasionally ventured into acting, with a 2011 appearance on RuPaul’s Drag U, and on The CW musical comedy series Crazy Ex-Girlfriend in an episode titled “I Need Some Balance” in January 2019.

Amram currently resides in Los Angeles. She has tweeted “Today was the day Donald Trump finally became president” every day since May 15, 2017. Her tweet on December 18, 2019 was sent at the exact moment Donald Trump was impeached and has since garnered over 95 thousand likes and 11 thousand retweets. However, she stopped after June 16, 2020, sent out an apology on June 17 for her past antisemitic and racist jokes and comments, and did not return to Twitter until October 27, 2020.

In 2019, Amram joined other WGA writers in firing their agents as part of the WGA’s stand against the ATA and the practice of packaging.