Assuming you are the only copyright holder on the code of the library, you can freely change the license that is applied to the library.
With the unlicensed version of your library, the rights of others are very limited. They may fork your repository (per the ToS of GitHub), but that is just about where it stops. People are not allowed to make changes or create derived works, which would include applications that use the library.
When changeing to the LGPL license, you give others more rights. They can make changes, as long as the changed version remains under the LGPL license, and they can use your library in applications of their own. Those applications can be closed-source applications (under condition that users of the application can swap out the library part for another version).