The URl you cite, https://www.loc.gov/catdir/cpso/lcco/, is the Library of Congress Classification system, not the Library of Congress Subject Headings. The LCC is used to create call numbers. LCC and LCSH do not have good correspondence.
If you are looking for LCSH, then you probably want http://id.loc.gov/authorities/subjects.html. That is a linked data system for LCSH. But you should be aware that there is no such thing as a list of "all Library of Congress Subject Headings". Many LC subject headings are constructed as needed by taking basic LCSH terms and adding geographic, topical, or free-floating subheadings. There is no compiled list of all the possible subject headings that can be created.
If you did mean LC Classification instead of LCSH, that is also included in the Library of Congress linked data system: http://id.loc.gov/authorities/classification.html.
Cataloging and Metadata Librarian
[log in to unmask]
From: Code for Libraries [mailto:[log in to unmask]] On Behalf Of Julian Gautier
Sent: Tuesday, January 24, 2017 12:18 PM
To: [log in to unmask]
Subject: [CODE4LIB] All LOC subject headings in a list or table
Could anyone here share access to all Library of Congress Subject Headings in a list or table? I was about to piece one together from the outline on LOC's website <https://www.loc.gov/catdir/cpso/lcco/> (it's also on different pages on Wikipedia), but figured you fine folks might already have a list.