Ok here we go. I'm sure I'll leave out some important details but if there is anything you have questions on, let me know.
Here is our victim, I mean lantern: Of course, with these, the first step you want to take is to remove the globe, globe ring and reflector. The globes are very hard to find so put it somewhere safe. Once you remove those pieces, turn the lantern upside down. It should look like this (hopefully yours is less sooty than mine): Note the 3 threaded studs sticking up around the burner. Those studs are what you want to work on next. The studs are threaded on both ends. One end is what you thread your globe nut onto. The other end threads up into posts that extend down from the fount. You may be able to turn the stud with just your fingers or you may need to get a pair of pliers (with some leather of course to protect the metal) and turn them with that. Regardless, they should come out fairly easily. Once you remove those studs, be careful when you are moving the lantern around as all that is holding it together now is a very thin copper fuel line. You don't want to kink or break that fuel line. Carefully lay the lantern on its side. Note the vented "collar" that circles the lantern below the fount: The next step here is to remove the two screws that hold that collar on the lantern. Take out the 1st screw. NOTE: With the 2nd screw, be CAREFUL when you remove it. The collar will have some "spring" to it and when you get that 2nd screw loose, if you aren't careful, it will launch the screw into the recesses of your workbench never to be seen again. There isn't a lot of spring there, but enough to launch a very small, very hard to replace screw. Be careful as you remove the collar. There are 2 things you need to watch for. First, the collar is held together by one very small strip of metal right where the control valve sticks out. It would be very easy to kink, bend or break that small strip so be gentle. Second, when you remove the collar, there are 3 rubber "grommets" that were held in place by the studs you removed in the first step. Those grommets are now loose inside the space between the lower part of the lantern and the fount. When you remove the collar, those rubber grommets will be free to roam and if you aren't careful to watch for them, they will join your collar screw in hiding. The other piece that is loose is a small 3 sided "box" with a screen on it. This assembly serves to cover the air intake tube and I would guess the screen is to prevent any large items such as june-bugs, etc from entering the air tube. Note the orientation of this box as it is tapered. The narrower end of the box should be in against the chimney if I'm not mistaken. Once you remove the collar and gather the grommets into a safe place, you'll see that there is a fuel line that goes from the fount to the burner. This fuel line (as mentioned above) is now the only thing holding the lantern together and as you can imagine, it creates a very delicate situation. Carefully remove the nut connecting the fuel line to the bottom of the lantern. Here is a pic of that assembly: Once you remove that nut, the lantern is now ready to be separated into 2 pieces. Next, you are going to focus on the valve. Remove the other nut holding the fuel line on the valve. NOTE: I would try to set the fuel line somewhere with the same orientation it had when you removed it from the valve. Both ends of the fuel line have the same size fitting but the fuel line needs to match up with the valve on the fount and the line feeding the burner on the bottom half of the lantern. Keeping this fuel line "oriented" to the way it came off the lantern makes life much easier. Otherwise you will be trying to figure out which end is which. I guess the other option would be to put a small mark with a marker on one end so you know which end goes on the valve body and which goes to the burner. Whatever works best for you, just find a way to remember; it will make things much easier in reassembly. Also pull the valve wheel off as the valve will not spin out of the fount with the wheel in place. It will hit one of the "posts" coming out of the bottom of the fount if you don't remove it. Once you get the fuel line off, you are ready to remove the valve from the fount. I personally like using a wrench and a screwdriver as pictured below, but use whatever method suits you. NOTE: Take note of the position of the valve BEFORE you start to turn it. When putting the lantern back together, you will need to line the valve back up in nearly the exact same spot so that the fuel line lines up with the burner connection. I would recommend you put a piece of masking tape on the fount and put a line on it so that when you reassemble, you can line the valve up with that mark. Also note that the valve has 2 different sized ends. It probably goes without saying but when you put the valve back in the fount during reassembly, the larger end of the valve will need to point out to accept the valve wheel assembly. Once you loosen the valve, it will look like this: The valve has an "F/A" tube of sorts connected to it. That F/A tube is removable and you shouldn't need anything but your fingers to unscrew it from the valve body. If you do need to use a tool, I would be very careful not to crush or bend the tube. It is a hollow tube and won't stand much compression. Once you remove the F/A tube, you will have 2 pieces like this: Note on the end of the F/A tube closest to you in the picture there is a very small screen. Do not lose this screen. It should slide off the end of the F/A tube opposite the end with the threads on it. DO NOT try to slide it over the F/A tube threads or you risk ripping the screen, etc. Once you remove the screen, note the very, very small orifice in the F/A tube. You'll have to look hard for it, but it is there. Many times, if your fount has any gunk in it, it will end up here. Odds are good that your screen and this orifice are plugged and I would recommend you clean them with carb cleaner and some compressed air (carefully). If you want to remove the "chimney" from the center of the fount, you can easily do that. There are two screws on the top of the chimney. Loosen those screws and you will be able to lift the entire chimney assembly up out of the fount. BE CAREFUL as there are some small spacers on the screws that may want to join the grommets and the collar screws in hiding so as you lift the chimney, watch those spacers to make sure they don't drop off the long screws. Additionally, the bail handle is easy to remove if you choose to do so. Just pull each side of it away from the fount and the ends should come out of their holders just like on a regular Coleman vent. In terms of cleaning, now is the time to do it. I would spend extra time on a BB shake for the fount and rinse and rinse and rinse. With the inverted lantern, your fount can never be too clean given the small screen and orifice assembly. Any flakes, gunk or otherwise in the fount will get sucked into the orifice and you will be reading these instructions again as you pull the lantern apart again. I would run compressed air through the fuel line, burner, etc. The check valve on these is not removable so just remove the pump and treat the leather cup as you normally would and give the CV a shot of carb cleaner if you want for good measure. The fuel cap is a 3 piece cap and you can replace that with a standard 200/220/228 size gasket.
Lanterns are like cats....if you have more than 3 in the house, people start to think you are a little weird.