Not sure what “Google JupyterLab” is. (Maybe this?) So I’ll answer your post title, " Import a local notebook to JupyterLab", demonstrating a path that works in the hopes it works where you wish, too.
Go to here and click on launch binder to spin up a temporary session of JupyterLab in your browser.
Drag-and-drop your local notebook from your local computer into the file browser/navigation pane that will be on the left side of the screen. After a second or so, it will refresh and show the local file you uploaded on the remote machine. Double click on the file in the file browser pane to open it and work on it, on it on the remote temporary session. Especially sincethe session is temporary, save anything useful you make by downloading it back to your local machine.
That was assuming by ‘import’ you meant ‘upload and use’. If you really wanted to import the notebook, there are options like ‘importnb’, see here. You can install it into the temporary remote JupyterLab session with %pip install importnb run in a cell.