You may know all this but in case it helps anyone someday:
Since it is skipping you might try thoroughly flushing it with a pen flush liquid first in case there is any residue left on the nib or feed from the manufacturing process.
A wetter flowing ink like Iroshizuku Take-sumi, Pilot Black, Quink Black, or Skrip Black could help mitigate other issues. What ink are you using?
If ink doesn't help perhaps the nib tines are too tight. Lamy or a nib meister should be able to easily fix this. Or you can too—if you've practiced on a number of cheaper pens first.
In my internet search for Lamy 2k issues, flow tuning seems to be one possible issue of several posited across various threads.
Some posters indicated that their pen needed a little more than usual pressure to deliver ink to the page. Or that upstrokes—usually much lighter than downstrokes—skipped.
I've tuned a few of my pens so they deliver a very fine, faint line of ink under only their own weight, but adequate ink flow under normal writing on downstrokes, so that the finer line appears on fast upstrokes of certain loops in letters like h or y. The result has been a reliable writer with subtle line variation.
On a few occasions I have observed pens with misaligned tines to skip. Again that's something that Lamy or a nib guru can fix. And so can you with practice.
If the pen suffers from baby's bottom it will tend to hard start when first starting lines, in my experience. This issue makes printing is a nightmare while cursive is less annoying. The hard starts may only appear after pausing cursive writing for a few seconds.
By contrast, skipping in the middle of a continuous line (of cursive writing, say) would likely be a flow issue, I think.
Hope this is helpful.
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