MultiViews automatic precompressed gzipping
 

I have a folder with two files: test.css and test.css.gz.

Browser requests test.css
Apache checks if browser can accept gzip compressed files
Yes:

Apache checks if a precompressed file exists:
Yes:

Apache serves the test.css.gz

No:

Apache gzips test.css

No:

Apache serves test.css ungzipped

I want to be able to do that in Litespeed.
I have tried to do this with RewriteRules and stuff, the problem is that litespeed gives the wrong headers, instead of Content-Type text/css Content-Encoding gzip it gives Content-Type gzip. This might be my fault, but I have no idea how to fix this.

No need to do that, LiteSpeed create gzip cache for static files, just let LiteSpeed do that automatically.

Well then, how DO I enable gzip compression with the static gzip cache from a .htaccess file?
I have tested

SetOutputFilter DEFLATE

and/or

RewriteRule . - [E=no-gzip:1]

and/or

mod_gzip_on Yes
mod_gzip_item_include mime text/css

There is no information about enabling gzip in your wiki, and the search function in your documentation gives a 404.

You can only disable gzip at directory level, not enable.
gzip should be enabled at global level in LSWS web console.

LSWS web console is the best option to gzip it. try it. and let me know

I don't think you're going to save much though; with modern web servers, the cost of compressing the content on the fly is negligible