On the template documentation page https://en.wikipedia.org/wiki/Template:Graph:Lines/doc the simple graph pulling data from wikidata works just fine, but the more complicated query times out.

This has come up at https://en.wikipedia.org/wiki/Wikipedia:Village_pump_(technical)#Problem_with_Template:Graph:Population_history and seems to be related to the wikidata query. That template at https://www.mediawiki.org/wiki/Template:Graph:Lines does a wikidata lookup from the documentation page. Though once it has done it in preview the page seems to remember the results.