Q. How can I tell if a journal article/ research article is peer reviewed?

There are a number of ways to find out.

1. Visit the journal's internet site. For item one, the journal is The Lancet. (Just google "the lancet"). Look for an "information for authors" page: http://www.thelancet.com/lancet/information-for-authors. To save time, you could control-f on the page and search for "peer review". Because different journals are arranged differently, finding this information can be a little tedious.
2. Look up the journal in Ulrichsweb, which contains information about nearly every journal published in the last century. When you find the journal name, look for a strange icon that looks a little like a referee's striped jersey in one of the leftmost columns. This means "refereed," which is another term for peer-review. (If you're in doubt about the icon, hover over it, and it will say "refereed.")
3. Instead of open web searches in Google, use an appropriate database through the library website. It looks like you're researching mental health of refugees, so you could use either PubMed or PsycInfo. Both identify whether a publication is peer-reviewed. (You can even use a checkbox to limit the search to articles in peer-reviewed journals.) But since you've already found these articles, it's probably quicker now just to use methods 1 or 3. In the future, though, use databases & eliminate a step.

NOTE: Just because an article is in a peer-reviewed journal doesn't always mean that article was peer-reviewed. Peer-reviewed journals often contain content that is not peer-reviewed: editorials, book reviews, letters to the editor, etc. If the article is in a peer-reviewed journal and is conveying original or secondary research, chances are it is a peer-reviewed article. When in doubt about a particular article, consult with your professor.