When I lived in a rural area temporarily as a young adult, people would refuse to use the telephone during thunder storms for fear of electrocution. This sounded like another old folk belief to me, but I never looked into it. (Growing up in suburbia, nobody ever said anything like that.)
I'm sure lighting could probably short out your phone, but phones are generally made of plastic, so I can't really see them causing much damage to you. Maybe make a loud noise and damage your hearing?
According to Snopes, lightning kills, on average, one person talking on phone each year.
Details here