Stanley lied in order to spare his mother pain and worry.
In the story, we learn that Stanley has been sent away to a camp for "bad boys." At Camp Green Lake Juvenile Correctional Facility, Mr. Sir tells the boys that they are responsible for digging one hole each, every single day.
"You are to dig one hole each day, including Saturdays and Sundays. Each hole must be five feet deep, and five feet across in every direction. Your shovel is your measuring stick. Breakfast is served at 4:30."
On Stanley's first day, he begins to realize how difficult it is to dig a hole that is five feet deep and five feet across in every direction. The surface (about eight inches deep) is the hardest to break through. By the time Stanley breaks through the surface, he has a blister on his right thumb. This makes it painful for Stanley to hold on to the shovel.
Unfortunately, the worst is yet to come. By the time Stanley is finished, his blisters have broken open, and his hands are openly bleeding. Every part of his body is aching. At the end of the day, Stanley is so exhausted that he can only stand still as he showers. He is too tired to lather up with soap.
So, this is what Stanley tells his mother when he writes to her:
Dear Mom, Today was my first day at camp, and I've already made some friends. We've been out on the lake all day, so I'm pretty tired. Once I pass the swimming test, I'll get to learn how to water-ski . . .
Stanley knows that he is lying, but his primary goal is to spare his mother pain and worry. From the text, we can infer that Stanley loves his mother and has a reasonably good relationship with her.