You need download the “mountain lion” first,
When you install mountain lion update, you might find the following is very helpful:
The software could not be verified. It may have been corrupted or tampered with during downloading.
open finder, go to applictions, find the macos installation package, Using secondry click choose “Show Package Contents” open “Contents” folder and then go to “Shared support” and open “Install ESD.dmg” double click on Install Mac OS X Lion and thats it,