I'm using Firefox on windows, I don't have binary component installed but Copying Password works for ME. Here's something you could try:

Go to a site with saved passwords e.g. http://news.ycombinator.com

Lastpass icon changes to show you have an entry. Click the icon, click "Show matched sites." Hover over the entry and you'll see three buttons: Copy username, Copy Password and More options.

I'm assuming these buttons don't work for you. Right-click instead on the entry and you should see a menu with the following items: Autofill, Copy username, Copy password, Copy URL, Go to URL, Edit, Delete.

Try the copy password entry. Hope it works for you.