Its still unclear to me if you have either LSWS or OLS installed. Upon your screenshot, you have the Directadmin Plugin for Litespeed installed. And a wordpress cache plugin. Nice. But no info about the Litespeed Webserver Software itself. The plugin is NOT THE SAME as the webserver software LSWS or OLS. Also, your screenshot says "Litspeed is not running. Apache is not running". That makes me wonder if LSWS or OLS is installed at all.
But nonetheless, lets assume you have OLS installed. First, you must start the service, so that the message changes from "Litesped is not running" to "Litespeed is running". Or ask your hoster.
Then you have to check if OpenLiteSpeed is configured to autoload .htaccess from directories and subdirectories automatically.
You can do this from the Webadmin Console:
openlitespeed.org
Here in the console, you have to look for the htaccess settings:
Using Rewrite Rulse with OpenLiteSpeed
openlitespeed.org
If confirmed, that OLS is running and htaccess autoload is correctly activated (and dont forget to restart OLS if you just activated htaccess autload), then its time to look at the redirects.
The redirects from OLS differs slightly from the apache rules, and especially for 301 redirects or rewrite bases, you have to make minor changes to the rewrite rules:
Using Rewrite Rulse with OpenLiteSpeed
openlitespeed.org
Using Rewrite Rulse with OpenLiteSpeed
openlitespeed.org
Redirect to HTTPS:
RewriteCond %{SERVER_PORT} 80
RewriteRule ^(.*)$
https://www.your-domain.com/$1 [R,L]
Redirect www to HTTPS:
RewriteCond %{HTTP_HOST} ^www\.your-domain\.com
RewriteRule (.*)
https://your-domain.com/$1 [R=301,L]
... or here another thread and short explanation from the LS boards:
Hello, I recently setup an OLS server (1.4.41) on Ubuntu 18.04 w/ LSPHP 7.2 running WordPress (WP) and it works great, however redirect 301's are causing me some headaches. Rewrite is enabled, and LSCache is installed on WP. It works fine and the rewrite to remove WP index,php is working...
forum.openlitespeed.org
Only rewrite rules work in .htaccess with OpenLiteSpeed. "redirect 301" may not work with OpenLiteSpeed in .htaccess(it works with LiteSpeed EnterPrise). hence, you may use rewrite rules instead. For example:
RewriteEngine on
RewriteRule ^old/file-name.php
https://domain.com/new/file-name [L,R=301]