Hi Arno,
Looking at the rewrite rules it appears they are looking for the “local.mysite.com” domain before they perform any rewriting. If you change your domain to something other than “local.mysite.com” using the Go Live plugin or any other method of updating the domain, the rewrite rules will no longer function.
To allow the rewrite rules to function after a domain change you may remove the following line. RewriteCond %{HTTP_HOST} ^local.mysite\.com
If you have updated your local environment to same domain as the live server the rewrite rules will no longer work regardless of the above suggestion because the rewrite rules will redirect back to your local environment and still not find the images.
One approach for making the rewrites work is to add a secondary domain to your live server, something like “images.mysite.com” which points to the same location as the main domain “mysite.com”. If you then update the rewrite rule to point to it, you can switch your local to your live domain and still load the images.
Update
RewriteRule ^wp-content/(.*)$ https://mysite.com/wp-content/$1 [NC,L]
To
RewriteRule ^wp-content/(.*)$ https://images.mysite.com/wp-content/$1 [NC,L]