Sign-up on en.gravatar.com is for free and lets you add files from your local storage or an URL. It is important to choose an image that meets the G rating (concerning audience types). After having added an image successfully, it may take some minutes for Gravatar to update.
In order to make sure to see it on The Lacuna Expanse as well, refresh the chat page and clear your web browser's cache. In case your new image does not show up after 15 minutes, make sure that your profile information includes a valid e-mail address (menu profile>player), verify your Gravatar settings and possibly re-upload the same file again due to technical reasons.
Screenshot of gravatar GUI: