Today anyone can sue for anything. But just because you can doesn’t mean you should.
To sue ADP for age discrimination would be a huge waste of money and time because you won’t win.
All of these layoffs are carefully planned and thought out. Each time a layoff is done a list goes out to those affected and they always include people of various ages and job titles so they are not targeting in specific group. There is an entire legal department armed with a bunch of smart lawyers ready to jump on any lawsuits that are filed.
The last thing to mention is when you get layed off in order to get any severance package they are offering you need to sign a waiver that says you will not sue for any reason either now or in the future.
Good point by @OnQ0oB7-5Lcya.