From the point of view of the libertarian socialist or social anarchist Left, "left-libertarian" means anti-capitalist, socialist libertarianism. "Left" refers to the struggle for social justice and equality. Because capitalism is a system of oppression and exploitation, we can speak of the masses fighting for their liberation from it. It's really about whose liberty you are concerned about. The libertarian socialist Left is concerned with the liberty of the working class, the oppressed. The libertarian Right is concerned with the liberty of capitalists, owners of property, landlords, bosses.
However, within the pro-capitalist libertarian right, "libertarian Left" I believe refers to those who are more minarchist or statist, that is, they acknowledge a role for the state. This is a mistaken use of the word "Left" though because "Left" doesn't necessarily mean statist. Social anarchism is antistatist but left and anti-capitalist.
The word "libertarian" was first coined by an American libertarian socialist back in the 19th century.
The emancipation of the working class must be the work of the workers themselves.