I used this expression the other day with a client, and he said he uses it, but his wife recently had said she'd never heard of it and didn't know what it meant. So he and I discussed what it could mean, its origin, and thought maybe it was a telephone line or a telegram... but we were both wrong.
Just now checked, and this is a very old idiom:
drop a line. Correspond, write a short letter or note. For example, I hope you'll drop me a line soon. This idiom uses line in the sense of “a few words in writing,” a usage first recorded in 1647.