Ceople, including workers, usually lie for the same reason that Adam did in the third chapter of Genesis: to stay safe and to shift any blame to others. It's a human thing Ask any cop you know how often s/he has heard the phrase, "I'm going to tell you the truth this time, officer."
What are they afraid of?
Punishment. Looking bad. Getting on the wrong side of the boss or co-workers. "Getting in trouble." There's a whole range of things that humans are afraid of.
Does being late represent a bigger issue? If so, what? (OK, that's two, but they go together.)
Maybe, but that will vary from individual to individual. Usually one lateness is not a big deal. A pattern of lateness would be.
Lateness could also be a symptom of something else. Consider a parent who suddenly is responsible for getting his/her child off to school. Think about a person who's been up all night worrying about a medical test result and so overslept.
What might a boss do to eliminate this problem?
First, you'll never eliminate individual instances of lateness because "stuff happens." Aiming at that target is a recipe for failure and frustration.
Here's how I suggest to readers and trainees that they handle issues like this.
Use the occasion of noticing that someone has come late as an opportunity for contact. The way you talk about this can make all the difference.
Instead of asking, "Why were you late this morning?" say, "I noticed you got here about 9:30 this morning. I think Jennifer was looking for you to ask something. Is everything OK?"
The rule is to describe the behavior specifically and follow that with the reason it's worth discussing. The response you get may be, "Yep, everything's fine, I just overslept." It may be, "There was an accident on the expressway." Or it might be, "my wife's sick and I had to take the kids to daycare." Any of those can lead to more discussion.
Like most single incidents of things that are not permitted, a single incident of lateness is usually handled informally. I call that "in the cracks of the system."
What if your subordinate is late for the third time in two weeks? I teach my trainees and audiences that the boss's job is to spot the trend, remind that it's not acceptable behavior, and give notice that future incidents will be documented. I call that a Transitional Interview, the bridge from informal supervision to formal.
Most of the time, for most people, that notice will be enough for the problem to go away. If not, you've got to document the behavior and try to get to the root of the problem.