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:

https://docs.litespeedtech.com/lscache/lscwp/cache/#purge-all-hooks