In the Lost series, a young guy named Charlie has a tattoo on his arm that reads "Living is easy with eyes closed". Does it carry any significance within the series or is it a real actor's tattoo?
According to Lostpedia, the tattoo belongs to the actor and not the character.
The words are a line from Strawberry Fields Forever, by the Beatles.
Charlie (as well as the actor who portrays him) bears a tattoo on his left shoulder which reads "Living is easy with eyes closed". This is a quote from The Beatles' song "Strawberry Fields Forever," a song whose lyrics and/or meaning could be considered symbolic of the Losties' experiences, Charlie's in particular.
As others have mentioned, the tattoo actually belongs to Dominic Monaghan.
However, to answer your other question:
Does it carry any significance within the series...?
Yes, it does.
Eyes, and in particular, opening and closing eyes, are a significant theme in LOST.
Charlie, in fact, would later die with his eyes closed,
as shown here:
So his tattoo is either
ironic, because he dies with his eyes closed, or literal, because dying with his eyes closed allowed him to "move on" to the afterlife.
It may not have been intentional, but it fits in very well.