Currently, it's not possible to have the character doing a simultaneous action while lipsyncing. As a workaround, you can have one character doing the lip-sync (like a narrator), while another does the action.

If you'd like this to be available, we highly recommend checking out our Feature Request page here -

You can post your requests and based on the number of up votes we'll decide on which ones to prioritize for a future Toonly update.