I Need Help Please L In Liberty On LMC

There are a few reasons why this might happen and without seeing the cent it's hard to give you an exact answer.

However, probably the most common cause of this kind of thing is a worn out die. As the die pounds out a coin, the forces involved in the collision between die and planchet travel laterally along the face of the die towards the edges.

That means that after 250,000 or so cents the die has changed and the devices have started shifting towards the edge of the coin.

After 500,000 - 700,000 coins the die are in even worse shape and sometimes the devices can blur into the rim or disappear partially.

Look up "Very Late Die State" or VLDS in the search box and you'll get tons of pictures.

It would have helped if you would have said what year your LMC was.
In the earlier years the L almost touched the rim to start with.
When the die was revised, it was moved slightly away from the rim.