I advocate using humor in writing, even in business writing—when it is appropriate. Used judiciously, it can lighten a fraught situation and relax your readers. The problem is that in writing, readers have only your words to go by.
On the telephone, they have your words but can also hear your tone of voice and inflections, which will help to guide them. In person, the people you are addressing not only have your words, tone and inflections but also your facial expressions and body language. Given the whole picture, it is far easier for them to understand when you are being funny.
In writing, something you state with a humorous intent might come across as sarcastic, snarky or downright nasty, even though that was never your plan. I advise that if you have any doubts about trying to be funny in a particular situation, play it straight and leave the humor for your face-to-face encounters.
And please don’t signal your attempts at humor in writing with LOL or ;- ). You want to come across as a professional, not as a 12-year-old.