ESI does not use a special cache type and therefore there is no “ESI cache”. ESI behaves like a hole that may have different cache criteria than the surrounding content. An ESI hole cannot be warmed up because LiteSpeed LScache is an http or URL based cache and an ESI hole does not have a URL that can be requested to warm up the cache. The TTL for ESI in the Cache plugin for Wordpress is hardcoded and cannot be changed.
@AndreyPopov You're confusing something. Since there is no setting in the cache plugin for Wordpress to change the TTL for an ESI hole, your incorrect comment refers to the TTL for the private cache and not to ESI. A private cache is not also ESI. Also, your statement that you could warm up "ANY" cache is wrong. The cache used in an ESI hole cannot be warmed up. Especially since this cache is usually private or no-cache.
@tryol0 You should give us more information about the CMS used and about the cache plugin because there is not just 1 LScache plugin and every cache plugin is different.
As long as you just shout, no one will talk to you. The const.default.ini can be changed, but it will be overwritten with the next plugin update. So what are you giving advice that doesn't help anyone. Especially since it is not a good idea to change the TTL for ESI cache because it leads to malfunctions. Exactly for this reason, the option to set the TTL of the ESI cache was removed from the plugin for Wordpress.
You give information about ESI even though you don't know what ESI is because you can't use ESI. Why do you write that ANY cache could be warmed up, which is not possible with ESI.