I believe I followed this wiki to install LiteMage for Magento 1, however, I still can not see “X-LiteSpeed-Cache: hit,litemage” header? Why?

There could be due to various reasons. It could be some important steps which might have been missed. It is worthy to check the following again:

• Do you have LiteMage enabled for your license? For 1-CPU and lower licenses, you will need to purchase litemage as an add-on, while LiteMage starter license has been included in 2-CPU and above license automatically. If you just recently upgraded your license by adding LiteMage, you will need to register a new license key through bin/lshttpd -r and restart LSWS.
• Have you placed “LiteMage On” in .htaccess?
• If you power your Magento store on a shared hosting service account, please contact your hosting company to ensure they enable LiteMage feature for your account.
• Have you/or your host set server level and virtual host level of cache root and cache policy?
• In “LiteMage Configuration” within Magento admin, has “Enable LiteMage Cache” been set to “Yes”?
• Has other full page cache been disabled?
• Has the “Enable LiteMage Cache Only for Listed IPs” been set while your IP is not in that list?
• For LiteMage to work correctly, you must have both “Configuration” and “Layouts” enabled under System → Cache Management. If you are using Magento Enterprise, you must also disable “Page Cache”.
• Did you try flush LiteMage cache and Flush Magento Cache Storage?
• Navigate to the app/ directory from ssh command line and execute the following command to see if layout/default.xml contains cacheable=“false”.

grep -r cacheable * | grep xml | grep false