This should not be a problem. The pro and the lite version are different and refer to different directories (wti-like-post-pro and wti-like-post) inside plugins folder. So if you simply overwrite the lite files, it may not work. If you do not need any data related to the lite version, then uninstall that and remove all its settings. Then freshly install the pro version, it should work now.
On the other hand, if it shows the pro settings on the plugin configuration settings page, then its not a problem in case it still shows wrong version.
Please let us know if you still face the issue.