Render one Paragraphs Module field value inside another Paragraph field's .html.twig template
You could try a template for the paragraph itself, rather than the individual fields. If you look in the modules/paragraphs/templates you'll see the default template used to render paragraphs. Copy this into your theme and rename it to paragraph--XXXXXX--default.html.twig replacing XXXXXX with the machine name of the paragraph. 

You can then access the values of your fields using {{ content.XXXX }} where XXXX is the machine name of the field, e.g. {{ content.field_list_item_link_url }}