What are these giant files in ~/Library/Autosave Information/?

Solution 1:

Delete them, they are just caches for an app or an installer.

A lock file indicates that a process was using them while it was forcibly quit or crashed. Normally, when system processes modify files, they create a lock file for it so that no other process can access it. These files are deleted when the process exits or stops modifying the said file.

The presence of the lock files indicates that their process has not accessed them since they were created. That means you have probably not used the app involved.

Source: https://superuser.com/questions/313878/what-is-a-lockfile