How to talk to a friend about "lack of control" in what happens to her son? I know a friend, who doesn't practice buddhism, and who is always worried about her young son. She is always concerned about everything that could go wrong, or things which could happen out of her control that she can do nothing about.

I've always been one who doesn't worry about the things that are out of my control, but I don't think that simple piece of advice is enough for her to act on it. I'm sure it's something that is "easier said than done".

What advice can be found in buddhism for this situation?
I suppose it largely depends on how close you are to her, or how seriously she would take and act on any advice.

These types of neurotic/anxious behaviors aren't something that are going to disappear by themselves overnight, or by you citing some scriptural passage to her that makes her see the light (most likely, there are cases where people do become enlightened in the scriptures from hearing verse, but in practice this is the exception not the rule).

The most practical way would be for you to, depending on the type of friendship you have, introduce the idea of meditation to her. Spin it in such a way that she is able to see that it doesn't have to in any way be connected with a "religion" or sectarian ideology. 

I don't know what your experience with meditation is, but if you have some then you have even more authority it explaining to her that meditating will allow her to see experientially that things are largely uncontrollable, and that all she is doing is creating her own misery in worrying about these uncontrollable things.

Perhaps even convince her to go to a retreat with you, if at all possible :)

Ultimately, you can lead a horse to water, but you can't make it drink. If she isn't ready to hear this, all you'll be doing is blowing hot air into the room. The best way to show others the benefit of meditation is to live your life as an example of the benefits of it.