What does the LOST.DIR folder contain? Whats the use of LOST.DIR folder actually?
why does is automatically appear after every reboot?
The Lost.dir is a system folder. Its a place where the Android OS places files that were recovered during a system boot up.

lost.dir in android



What is the folder for? 


  Its quite evident that there is no application named LOST.DIR
  installed on your device. At times the folder's size can range in
  gigabytes. In such situations one may wonder about the contents of the
  folder and its use, and whether it is safe to delete the folder to
  save memory.




Can I delete the contents of LOST.DIR ?


  In order to save precious memory space its completely normal to delete
  the contents of LOST.DIR as it only acts as a recycle bin. You can
  also delete the LOST.DIR folder itself but it will reappear the next
  time the system boots up. When your Android system throws up a message
  saying 'Preparing external SD card' its actually checking the contents
  of LOST.DIR, and if it fails to locate the directory, it creates one.




ref :
All you need to know about LOST.DIR folder on Android devices