The previous posters don't know what you're talking about because your gun is defective and theirs aren't.
It is both a gun and a magazine issue.
The original LCPs don't have the problem but some of the later ones do.
Ruger used to ship LCPs with Mec-Gar Italian magazines. These go in perfectly with older LCPs and okay with newer LCPs that have the issue, but they are very hard to find.
Now Ruger ships LCPs with their own magazines and they seem to exacerbate the issue.
If you can track down older Mec-Gar magazines that would be the way to go.
I sent an LCP in to Ruger with this issue and they were HOPELESS. I sent them a really nice diagram explaining the issue and they just returned it saying they shot it and it functioned fine. No kidding, I knew that. I said the magazine doesn't insert correctly. They probably just don't have an easy way of fixing it.
I'd just sell the gun or make Ruger take it back.