The hook that you are using is not the issue - how it is secured in the dry wall is. I am guessing your lanterns are probably 4 lbs - you can check by standing on a scale with a lantern and then getting on the scale with out the lantern and subtract, the difference will be the lantern weight.
Something like this should do it, you will notice the grip mechanism that fits above the drywall - screw in type swags do not have the necessary grip and weight distribution to hold that kind of weight and also handle the lantern being touched or moved.
If you perform a search you might look for Toggle Wings or Toggle Bolts. Added above to the answer per comments. 6-19-2018