I have a couple of lanterns now mounted on the house both running CFL lamps, details as below.
A local lantern that was originally pole mounted so I had to make an adaptor to enable it to fit on the wall.

The lantern is a late version of the Beta 4 from the 1980's, it was designed to run GLS and has a bayonet lampholder. This version of the lantern has no refractor ring or refractor on the bowl so is completley clear. The lamp came with a domestic CFL lamp installed as can be seen above. The bracket was rusty so was cleaned and painted while the lantern just needed to be cleaned and polished to remove marks from the canopy. The cable hanging down is ready for a photocell to be added.

The lamp fully restored and PEC fitted above the bracket, the bowl has been treated with a frosted spray coat to hide the appearance of the CFL Lamp. The lamp gave a rather yellow appearance so was replaced with a behive shape 32W CFL which runs at a colder colour temperature of 6400°K, ideally i would like to run a 4000°K lamp but they are hard to find in a decent wattage.
A local lantern that was originally on a wall bracket and removed due to faulty control gear.

I was curious to see how the Beta 5 that was designed to run a 35W SOX lamp would look with a CFL lamp installed, so I purchased a 68W lamp which when compared with the domestic 20W lamp next to it looks rather large.

The lantern is an early 1980s example as the control gear is on a short lengh housing, later models are the full length of the housing. The lantern was in physically good condition, a good clean and polish and the lantern looks almost as good as new. The control gear was removed and the retaining spring was altered to support the larger girth of the CFL when compared to a 35W SOX lamp.

The cover is replaced and the lantern powered up. This photo makes the lamp appear a little yellow, in reality it is a warm white though not to warm as some CFL's have a tendency to be.

The Lantern is mounted on a corner bracket and powered up. The lamp suits the beta 5 very well. The output is quite impressive giving a similar lumen level to that of the SOX version. the light quality is similar to that of a Halogen but with a wider spread. The refractors on the bowl do a good job of providing diffused light.