The lol given in a text or IM in response to a message that's not funny, but requires a response to be courteous. Like the "courtesy laugh" in conversation.
"Her text was confusing.... so I gave a courtesy lol."
To use the phrase lol when you get a text message that is supposed to be funny when it actually isn't normally sent to a girlfriend so she doesn't mad, you also may expect getting at least a courtesy lol when sending something funny to someone else.
Frank: "Did you send that funny cat pic to drew yet."
John: "Yeah he didn't even give me a courtesy lol."