How to deploy a C# WPF app with a sqlite database?

I don't think it's all about making the installation file. I think, the application crashes because the software can't find the database. If you develop your software in such a way that, it creates the database (if it doesn't exit) on startup, the way you create the installation file won't be a problem. Here is what I mean:

//use an environment generated file path.
public string _dataBasePath = $@"{ System.Environment.GetFolderPath(System.Environment.SpecialFolder.ApplicationData)}\databaseName.db";

Using an object relational mapper like NHibernate. You can override OnStartUp and create your database:

   // In the App.xaml.cs class
    private override void OnStartup(StartupEventArgs e) {
        base.OnStartup(e);
        BuildSchemaAction(config);
    }
    private void BuildSchemaAction(Configuration config) {
        new SchemaExport(config).Create(false, !File.Exists(_dataBasePath));
    }
    protected Configuration config = new Configuration();

The database file (since it is SQLite) will not exist, so it will be created. Subsequently, it will not be created. The _dataBasePath field will be the path in the connection string, in order to access the database in the path it was created.

x.ConnectionString = $"Data Source={_dataBasePath};version=3";