Past

Adam and Lilith, the first humans
From the dust of Earth, Adam and Lilith were the first humans created by the Angels, made to be equal and lived in the Garden of Eden. However, Adam wanted total control over Lilith but Lilith refused and left him. In the Garden of Eden she met Lucifer, and the two dreamers fell in love with each other. Lucifer, with Lilith, wanting to share the power of free will, offered Adam's second wife, Eve, the Fruit of Knowledge, with this act evil made its way into the Earth which subsequently created Hell. As punishment, both Lucifer and Lilith were sent to Hell,[1] where Lilith thrived and empowered demonkind with her singing.[1]
At an unknown point, she married Lucifer, and later had a daughter named Charlie with him.
Seven years prior to the series, Lilith left Pentagram City and hadn't been seen or heard from for seven years.[1] She left Hell and somehow was allowed to stay in Heaven, implied to be because of a deal with Adam.[2]
Hazbin Hotel pilot
Towards the end of the pilot's opening song, there is a poster that can be seen on the Clock Tower with Lilith's name and image mentioning a concert with the text "RESIST".
During the pilot, Charlie attempts to contact Lilith for moral support after her disastrous interview. Unfortunately, the call goes to voicemail, prompting her to leave a long message instead, mentioning that she knows Lilith is really busy.
Several photos of her can be seen throughout the Happy Hotel, most notably a family portrait that catches Alastor's attention.
Hazbin Hotel Season 1
"The Show Must Go On"

Lute demanding Lilith to stop Charlie
Lute confronts Lilith while she's lounging at a beach, and is told that if she wishes to stay in Heaven she must go to Hell and stop her daughter Charlie.