Customise standard lists within my shortcode

IMO you need to create individual shortcodes for UL, OL and LI to make it sample.

Shortcode for UL.

function shortcode_ul( $atts , $content = null )
{
     return '<ul>' . do_shortcode( $content ) .'</ul>';
}
add_shortcode( 'ul', 'shortcode_ul' );

Shortcode for LI

function shortcode_li( $atts , $content = null )
{
     return '<li>' . do_shortcode( $content ) .'</li>';
}
add_shortcode( 'li', 'shortcode_li' );

Use

[ul] [li]Unordered[/li] [/ul]

It should output

<ul><li>Unordered</li></ul>

Note: Add attributes as per requirement. E.g for CSS class <li> use attribute class. It’ll be more flexible and extendable.