This is a traditional lighting problem that goes back to the beginning of cinema and there are a number of tricks, some may look better than others depending on the camera set-up.
1) Use the actual light from the flame as the source. Requires very fast lenses and really high ISO ratings but obviously it would look natural, though the flame will be quite overexposed if you are exposing more for what the flame is lighting, i.e. his face. When the face is very close to the flame so that both are in close-up, this may be the best technique though and if the face is close to the flame, then the exposure isn't so hard to achieve.
2) Use an electric bulb inside or outside on the lantern. I've done plenty of shots when the lantern is sitting on the table, for example, of hiding a light bulb behind the lantern and using some black wrap or some black paint on the opposite side of the lantern glass to hide the bulb from camera and point the real flame side towards camera. Or I've just installed a light bulb inside the lantern and frosted the glass to hide the bulb (it helps to use a bulb that is flame-shaped like a candelabra bulb). This works well particular in distant shots so that the lamp can actually light the actor.
3) Follow the actor with an orange-gelled spot light as if it were coming from the lantern. This works better when the lantern isn't moving and you can flag the light off of the lantern so it doesn't get front-lit (as in your example -- it would have been better to get more of the light flagged off of the lantern. Doesn't help that the metal is shiny and reflective.) Gets harder as you have to follow the actor around as he holds the lantern. This is classic old-school Hollywood lighting that you've seen even used recently, such as the scene in "Shutter Island" when DiCaprio is walking around with the match flame in the dark prison.
Here are some examples.
"Days of Heaven" used a battery-powered light bulb inside the lantern, frosted to hide the bulb:
"Amistad" here used an electric light inside the lantern but this design made it easier to hide the bulb:
"Snow Falling on Cedar" used a number of tricks in the opening scene, from using the actual flame, to hiding a bulb behind the lantern (as in here), to shining an off-camera light, even dimming one technique and switching to another during a camera move:
"Elephant Man" used an off-camera spot light, though in one angle in this scene, they switched to a lantern with a bulb inside, but only when the actor was blocking it with his body to camera, walking away: