One in three UK women (36%) have experienced online abuse at some point in their lives.
Social media companies are facing a legal requirement to regularly report on the steps they are taking to address online abuse against women and girls.
The Lib Dems will attempt to amend the Online Safety Bill to introduce the new law.
The Bill is an attempt by the government to police the internet by making tech giants legally responsible for keeping people safe online.
But Christine Jardine, the Lib Dem equalities spokesperson, said it was an “outrage” that the Bill “does not mention women even once”.
“This is a total dereliction of their duty to protect women and girls,” she said.
Under the legislation, companies will be required to be transparent about how they are tackling online harms and the effectiveness of their safety measures.
The amendment would force social media firms to make public what moves are being taken specifically to tackle content promoting or perpetuating violence against women, girls and vulnerable groups.
It comes ahead of International Women’s Day on Wednesday, which has the theme “DigitALL: innovation and technology for gender equality”.
According to Refuge, 1 in 3 UK women (36%) have experienced online abuse at some point in their lives - which is over 11 million women.
Of these women, 1 in 6 (16%) experienced this abuse from a partner or ex-partner, meaning almost two million women have been abused in this way.
A report from the charity found women are seven times more likely to experience sexual harassment on social media than men.
The amendment will be tabled in the Lords by former Lib Dem minister Baroness Featherstone.
In the Commons, Jardine has tabled a separate bill that would have the same effect.
She added: “Every day that the Conservative Government fails to act on this widespread problem is another day where big tech companies are not held to account on online abuse against women with victims left to fend for themselves.
“These pieces of Liberal Democrat legislation would ensure that women are not left abandoned to the wild west of online abuse any longer.”