This stumper is a children’s picture book that I think was published either in the late 80’s or the early 90’s.  I live in Australia, and I’m afraid I don’t know if it was an Australian book or not.  If it is I suspect it will make it even more difficult to solve!
I originally thought the title was “Lucy’s Beach”, but I’m obviously wrong about the name because I have not been able to find any record of it.  I am pretty sure it’s a girl’s name followed by the word “beach”.  I don’t know who the author is.
The story began with the main character, a young boy, in the kitchen at his house with his family.  The weather is good, and he comes to the decision that today he will cross the red cliffs to the beach.  His family listens to his announcement very seriously.  You got the sense that it was an important thing the boy was doing, and that it’s the first time since some kind of significant event that he was returning.
He leaves the house and crosses the cliffs.  He navigates the narrow ledges of the red cliffs and finally arrives at the beach.  He searches in the beach until he finds a stone covered by the sand, not red like the cliffs, but flat, smooth and polished.  It has a name engraved in the top of it.
Finding the stone makes him remember playing at the beach before with his younger sister, and the boy remembers his parents telling him to watch his sister in the water to keep her safe.  I think he got distracted playing his own games, and his little sister ended up drowning.  The stone is a memorial marker for her.  He lifts up the stone and finds a compartment with some kind of plant or flower seeds.  He removes the seeds from the box and blows them into the wind, and they rise up above the towering red cliffs.
I think that’s pretty much the end of the story.  Pretty sad for kid’s picture book.  I really hope you can help me solve the mystery of this stumper!  I’m certainly looking forward to hearing from you.