Google's John Mueller confirmed that they completely ignore the HTML lang attribute for determining the language and region of the page. John said this at the 55:54 mark into the video hangout from last week.
Instead, John said you should use hreflang markup.
The question was:
So how important is it to display in the HTML code, the language of the site, if you already declared it in Google Search Console, for example.
John Mueller replied:
We don't use that at all.
So we use the hreflang links if you have that if you have different language versions. But the language attribute within the HTML markup is something we don't use at all. We've found that this language markup is something that is almost always wrong. So we tend to ignore that.
They go on a bit more about the topic and you can watch it below:
Forum discussion at Google+.