PHP version 7.2 and above

is this amount (128mb memory) sufficient for most of other websites?

This is enough for most WordPress sites.

is this plugin really need to use so much (really don’t know is it too much or not) memory

The LCP plugin itself uses very little memory. The code is fairly light. However, this plugin is an interface to WP_Query – a built in WordPress mechanic to get desired posts. And it can eat up a lot of memory if you use it to fetch a lot of posts with plenty of content. So the amount of memory used while querying/displaying posts depends on what you are actually doing with the plugin. The more posts you display, the more memory is used, but there are also plenty of other factors that could increase memory usage: filters used by the theme or other plugins, posts’ size and so on. In your case, the file that’s trying to allocate more memory is meta.php which deals with metadata, like custom fields, so maybe your posts have a lot of data stored in custom fields.

in terms of memory that php needs; is it allocating that space from the RAM memory of the host device?

Yes, of course.

host says it is 128mb is max;
is it max for php? or their host service?

memory_limit is a per script limit, meaning it doesn’t regulate how much RAM PHP can use in total but it does regulate how much a single script (like your WordPress site) can use.

neutrally, or normally what is the up limit of max memory?

There is no upper limit, server admin could allow PHP to use all the available RAM, it would be stupid though 😉

So now that you know your PHP memory_limit is at 128 MB, go to wp-config.php and look for define('WP_MEMORY_LIMIT', '128M');. If it’s not 128M, update it to this value and see if your problem disappears. If it doesn’t, it simply means you should either edit your site to use less memory (less displayed posts) or find a more robust host.