According to my build of LFS-6.3 using the live-cd sleep is provided by LFS.
It is part of the coreutils package and is found in /bin.
It should also be present on newer versions like LFS-6.6:
file:///home/hoes/Desktop/book-lfs/LFS-BOOK-6.6-HTML/chapter06/coreutils.html.
But note that sleep is a bash program.
If you are programming in C++ you can't just call shell programs.
You need to use libraries with the appropriate commands.
Maybe this thread in the ubuntu forum is of use to you:
http://ubuntuforums.org/showthread.php?t=296142
It refers to a library that contains sleep and a way to create sleep using the time library.
Your question is more about programming in general than about LFS.
I hope this is helpful, but maybe it's also a good idea to look up a tutorial on c++ programming and library calls on linux.
Good luck.