Sometimes when a coin is struck a lot of greese is on the die, which can cause a coin to be struck without a letter or something of the like. It is interesting, but also common. I hope that this helps!
You mean the "P" in PLURIBUS? That's the only "P" I can think of that should be on the back of a Lincoln Memorial cent. If you're referring to the fact that there's no "P" beneath the date, on the front (obverse), then there wouldn't be, on a Philadelphia coin. They did not put the "P" mintmark for Philadelphia on cents. It's just blank. If the "P" in PLURIBUS on the reverse is indeed missing, then it is likely as @brandon spiegel said: a grease-filled die. Really impossible to say, without photos.
You just dated yourself with that seemingly-obscure reference, but I picked up on it for some odd reason (even though I never saw the musical or really listened to the music). Of course I'm just old enough to remember the time when you couldn't escape that on the radio and elsewhere. (I was in middle school.)
My phone doesn't take good pictures sorry will try again, but it has other varieties like the L is right on the rim almost disappearing and In God We Trust the letters are fat and somewhat smudged his ear is missing looks like he has an earring its round and filled. So are they errors or varieties ,will try pictures again. Thanks for the input .