By default, profile images are all cached when you use the LiteSpeed Cache plugin, which is why it is not reflected even after you upload a new picture.
There are a couple of solutions to this.
1. Turn off caching for logged-in users. (Not recommended)
2. We can use the options via the WordPress dashboard – LiteSpeed Cache – Cache – Purge – Purge All Hooks.
3. The hook that runs after we update the profile image is “xprofile_avatar_uploaded”, so add this hook to the list.

4. Don’t forget to click on “Save Changes” to apply the setting.
You can also visit their official documentation to learn more: