You are supposed to rinse out the nib and feed periodically. There are several ways to do it, but at least rinse the nib and feed until the water that drips out of the nib isn't obviously colored, soak it in some water for an hour or so to get even more gunk out, then put the nib point down on a paper towel or something to suck even more old ink out, and then give it some time to dry.

You don't need to do as much if you're just refilling it with the same color, but since you're running into trouble might as well rinse it out fairly well.

That just might fix the problem if it's built-up dried ink clogging up the pen.

I've had hit or miss luck with Lamy converters. In my case the seal in the back was letting in air and drying out the ink. I've found using a blunt-tipped syringe and refilling old cartridges works better. There's a bit more ink capacity as well.

FYI, Never had any issue with Lamy and their (official) converters (the only difference being that they carry less ink than a cartridge), no matter the ink brand I have been using. And I have been using Lamy since the late 90s.

• As suggested, you may want to rinse your fountain pen (and let it dry for a few days). You may also learn to disassemble the fountain pen entirely (which for a Lamy Safari means removing the nib and the feed) to do a deep cleaning (you will find guides on YT). When not using a fountain pen for a long time, ink can dry in it and should be cleaned (with standard ink, barely warm water should be more than fine)
• Waterman, like Pelikan, is a great (and cheap) ink, I've been using it since I was a kid (back in the 70s ;) but you may want to check what exact type of ink you're using. Make sure it is ink for fountain pens and not India or acrylics which would ruin any fountain pen.
• Another possibility: check you're using a genuine Lamy converter. There are cheap knock-offs. And just in case: don't try to use a Lamy converter on any other brand of fountain pen.
• Last suggestion: contact Lamy support. They're not the fastest but they're good. I had them help me with a 2009 model a few months ago, without any issue. I place them right next to Twsbi as far as customer support goes, and Twsbi is real excellent ;)

I prefer to just refill cartridges rather than try to use the converters. I have a small mountain of converters for all kinds of pens, all of them originally pack-ins with the pens themselves, and I've never used any of them.

Converters are full of seals, gaskets, and moving parts. All potential points of failure. A cartridge isn't. You can just refill it with a syringe and be on your way. For me, at least, I have the luxury of never being in a situation where I'll conceivably ever do enough writing in a day to completely run a pen dry, so I don't have to carry spare cartridges and thus don't need to jigger some kind of way to reseal them.

Many of my pens still have the same cartridge in them they originally came with. Some, like my Sheaffer Targa, have a cartridge in them that's easily decades old. No sweat.

Also, it's usually a good idea to flush out your nib and feed when you change brands of ink. It's possible, albeit unlikely, that some combination of ingredients in ink A could react poorly with ink B, and gum up and cause a clog.

@Shalaska
Ive just pulled out my one Lamy converter.
The converter in the photo does not look like a propriety Lamy converter, It looks like an International Standard converter. In which case that would account for leakage and poor performance.
Lamy. most of the Japanese, Shaeffer and a few other manufacturers use propriety cartridges and converters that are not interchangeable with other brands.
Some Chinese pen models claim to use Standard International cartridges but they are sufficiently out of dimension that only their own products will work.

I use a refillable cartridge and I've never had problems. Try a few different cartridges until you find one that doesn't leak. I would recommend one but it's been quite a few years since I bought it and I don't remember anything about it.

Also try a different ink, maybe? Some of them can leak easier out of the nib. Also clean your pen with some alcohol to make sure it isn't that.

When you are inserting the converter into the Lamy make sure you are inserting it into the correct slots so it fully engages (it can take a bit more force than you expect).

I made the mistake of using the half circle sections when I first got my Lamy Al-Star and it made a bit of a mess.