Can you cite the Library of Congress even though there is no individual author?

Yes, absolutely.

In author-first citation style, an institutional author can be the author.

The Library of Congress is the institutional author.

So you can write:

The Library of Congress (n.d.) describes formerly enslaved African Americans as free people surrounded by hostile whites and documents the subsequent resistance to their freedom, including the development of segregation and racial violence.

Or, if your reference list gives a publication date:

The Library of Congress (1998) describes the post-emancipation situation as one in which formerly enslaved people faced hostile whites and documents continuing discrimination and segregation.

The Library of Congress's own historical material states that formerly enslaved people faced “many hostile whites” and describes the subsequent erosion of their gains, including segregation and racial violence.

Important distinction

You can write:

The Library of Congress (1998) argues...

But because this is an institutional historical exhibition rather than an individual historian's scholarly argument, I would prefer:

The Library of Congress (1998) documents...

or:

According to the Library of Congress (1998)...

That better reflects what the source actually is.