How to pass data to javascript in custom widget class

This is a timing issue, as you can see from the hook order. By the time you get to the dynamic_sidebar function that executes your widget code on the front end, you are already past the widgets_init and wp_enqueue_scripts hooks (the dynamic_sidebar hook is inside the function with that same name). You cannot enqueue scripts from a widget.

There are two ways to get around this:

1. Write a function that accesses the widget data directly from the database (it’s a multidimensional array which you can find with get_option(sidebars_widgets). You can bind this function to the wp_enqueue_scripts hook.
2. In stead of properly enqueuing the script, just print it in the footer by using the wp_footer hook, which is still available when the widget code is executed.

By the way, wp_localize_script will work anywhere, as it just prints the variables the moment it is called.