I used a #3626c Trans-Clear Minifigure Head for the lamp and a black #4740 on top.

The right brown lantern is the design posted here, with 6 Base Flutes. Here I did mount a 5mm LED. The head does fit snug on the top of a 5 mm LED.

The left is the Lantern with 4 Base Flutes. Her i used a 3 mm LED then the Head is mounted on the stud of the post.