I'll be the first to say I'm not a professional lighter repair person and I do not really have a supplier for parts so this may not be as useful as it could be.
Ligne 1 Lighters
It is possible to take apart a ST Dupont Ligne 1 by taking the pin out of the hinge for the lid.
I have a set of micro-screwdrivers (this one here) and one of the tiny bits makes for a good pusher to push the pin through without damaging the lighter. Something like a paper clip will not be strong enough, it needs to be very thin and yet solid. If you mess this up, you will scratch your lighter so don't even try it if you're not sure.
Once you take the lid off you can now finally take out the flint pusher, it pulls out almost like how a ligne 2 lighter does normally. There will be a screw under it. This screw and the fuel nozzle itself act as the screws for the top portion of the lighter. Once they are both removed the top part of the lid will come off.
There's a few parts inside, but generally the flint release button will fall out and if it's a vintage ligne 1 there's going to be a long/thin metal spring plate which should be lifted by the flint button when it's up.
This metal plate pushes down the secondary fuel stopper which most older L1 lighters have when the flint chamber is open (the first being the lid of course). This mechanism seems to often malfunction, causing the lighter to basically act like it's out of gas or otherwise low on fuel, when really the mechanism is just cutting your fuel off due to wear. I am guessing this is why st dupont seems to have made revisions to this mechanism over the years, and supposedly some of the newer models do not have it at all like a ligne 2.
It's definitely possible to repair this mechanism if you had the right parts but unfortunately I do not. I have found a short-term solution though, which may be justifiable if your lighter has nothing else wrong, but basically if you loosen both the fuel nozzle and the screw which hold the top on, you can basically release enough pressure on the 2nd fuel stopper that it will then function more or less normally, except if you push down on the top of the lighter the flame will go out. You're basically pushing on the 2nd fuel stopper at that point. That's as good as it's gonna get without paying to get it fixed properly. Also, don't make it so loose that your screw or fuel nozzle falls out or you will be paying for that repair a lot sooner Also, any rubber parts can be greased with petroleum jelly to extend their life.
On my first l1 large I had a damaged refill valve and I had no idea how to get into the gas tank to fix that. I ended up sending it into Authorized Repair Service and they did a pretty good job at repairing it properly. The lighter works like a champ now, although it's kind of my "beater" as the plating is wearing off. Of course depending on the problem you might be able to fix it yourself. If it's just clogged or if the flame height adjuster is acting a little funny, you may be able to do some of the steps mentioned here, and also give the parts inside a good cleaning. a q-tip and water/alcohol is all you really need.
Ligne 2 Lighters
Ligne 2 lighters tend to be a little bit easier for the average person to repair. The entire fuel release mechanism is basically the flame height adjuster. This tends to be where the lighter will leak from when the o-rings wear out. If your lighter is leaking from the fill-valve, unfortunately I do not currently know the procedure to repair this. However, if it's only leaking from the flame-height adjustor, or seems to leak when the lighter is closed, but not from the fuel valve, this may be all you need to do.
Start by unscrewing the screw on the flame height adjuster. The gold/silver plated piece should come out and under it there's going to be a metal stopper around the shaft. This is the stopper which prevents you from making the flame too large, and will have to be reset manually. After this is removed, there should be 2 opposing metal blocks. Do not unscrew the center shaft yet, rather you must use either tweeters, or needle nose pliers, to spin the entire valve using the 2 metal blocks. This is the heart of the ligne 2. Note there may be a bag of charcoal floating around inside the lighter. This is normal.
Once the valve comes out, it has a few o-rings on it, all of wish should be rotated/flipped and lubricated with petroleum jelly before re-assembly. Don't use a ton, you don't want it getting all over the place, just enough to moisten the o-rings and keep them from cracking. You can also further disassemble the valve for cleaning, the stopper mechanism at the top can be unscrewed, inside it are a few very small filters which, you can flip around the other way or replace if you can find suitable material. The actual valve stem on the bottom can also be unscrewed fully now that the entire valve unit is removed, and this area can also be cleaned/adjusted as necessary. In my case, the main fix was rotating the outer o-rings and lubrication and avoid over-tightening of the valve stem. The rest seemed to be working fairly well. Important, if you do remove the valve stem from the entire valve unit, be sure not to over-tighten the flame height valve stem! If you do this, when you screw in the entire valve unit, you'll be unable to adjust your flame height without accidentally unscrewing the entire valve unit from the lighter, which will definitely make it leak.
Afterwards, it's time to put the valve unit back into the lighter. Be sure the bag of charcoal isn't in the way and re-insert the valve into the lighter. Ensure the lighter's lid is open and tighten it carefully with tweeters or needle nose pliers. If you try doing this with the lid closed, the valve may not tighten all the way into the lighter, or it may feel like it's tightened all the way when it isn't. After it's all the way tightened, make sure the flame height adjuster can still move freely without rotating the rest of the valve assembly. If so, it's almost time to fill the lighter. Close the lid and put the flame height adjuster as low as it can go without getting it stuck tightly. Fill the lighter and try to light it up, adjusting the flame manually if necessary to ensure it's not just too low. If it's not leaking at this point, you can now put back on the flame height stopper. There's no perfect way to do this, just make it so that the flame can't get ridiculously large and it should be fine. Once you've got the stopper set, you can finally put the cap back on and screw it down reasonably firm, but make sure you do not tighten the valve stem into the valve unit while doing it. Now you should be able to adjust the flame height as normal.
I should note that it seems the yellow refill valve on the ligne 1 small and the ligne 2 and the green from the gatsby are a bit more durable than the red. This seems to be because the yellow/green lighters have a rubber o-ring and don't require the dupongaz to puncture the valve to make a seal. The red valve on the large l1 actually requires the valve to break through the plastic end of the dupongaz, the yellow/green ones instead have a metal piece which gets pushed in by the lighter itself, rather than pushing on the valve, then seals against the rubber washer. When the spring in the valve wears out, yellow/green lighters can still generally be refilled for quite a while, it'll be loose but it may not leak, the red-refill lighters will fail a lot sooner than the yellow. Luckily, there is a workaround. Get one of those butane adapters off ebay for the dupont lighters. They don't require that the valve break through anything and will allow you to continue to refill your l1 without breaking the valve off. These adapters typically come with a rubber washer to seal to the lighter, in a slightly different manner, but a seal none-the-less. Just make sure you use good butane (vector or lava). I'd anticipate that eventually the spring will just become completely worn and the lighter will stop holding gas at that point. That's when you definitely need to send it in. If there's any signs it's leaking fuel from the refill valve I'd definitely get it repaired professionally.
It is possible to buy extra spark wheels and lighter refill caps from the site elegantlighters.com which is basically the store of authorized repair service. If that's all you need, then that's an easy enough fix. they also sell flints and i do recommend you use duponts flints, they are actually very good flints and i've found most other ones will not work as well and will actually wear out the flint wheel faster.
All rubber parts can generally be greased with petroleum jelly to extend their life. You don't want it drenched on there, just enough to moisten the o-rings. Also, petroleum jelly is also useful for the refill cap (and flalme adjuster on a ligne 2), if the pull-out tab is real loose and falls down without any intervention, apply some petroleum jelly around the hinge and push the tab back down into it. It should stay in place for quite a while after doing this, even after repetitively pulling it down and pushing it back up. Re-apply every few months/years if necessary.