Reinstall Mac OS X Lion 10.7 : Error message

Why don't you try:

1. Restart the computer. Immediately, at or before the chime, hold down the (Command-Option-Shift-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the target drive (out-dented entry w/type and size) from the side list.
5. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs, only if installing Mojave or Catalina ) or Mac OS Extended, (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Install OS X and click on the Continue button.

This should install the original version of OS X that came pre-installed from the factory.

I would guess that all four keys were not fully depressed during the startup. Instead, it was booting from the local startup drive which had no installed system.

Do you have a working copy of the Lion installer? Have you set the date back? If you have the Lion installer, then you can create a USB flash drive installer.

Make A Bootable Lion or Mountain Lion USB Installer

1. Get a USB flash drive that is at least 8 GBs. Prep this flash drive as follows:

1. 1. Open Disk Utility in your Utilities' folder.
   2. After DU loads select your flash drive (this is the entry with the mfgr.'s ID and size) from the left side list. Click on the Partition tab in the DU main window.
   3. Under the Volume Scheme heading set the number of partitions from the drop down menu to one. Set the format type to Mac OS Extended (Journaled.) Click on the Options button, set the partition scheme to GUID then click on the OK button. Click on the Partition button and wait until the process has completed.
   4. Select the volume you just created (this is the sub-entry under the drive entry) from the left side list. Click on the Erase tab in the DU main window.
   5. Set the format type to Mac OS Extended (Journaled.) Click on the Options button, check the button for Zero Data and click the OK to return to the Erase window.
   6. Click on the Erase button. The format process can take up to an hour depending upon the flash drive size.

2. Insert the Lion DVD into the computer's optical drive. 

3. Plug in your freshly prepared USB flash drive. You are going to clone the content of the InstallESD.dmg disk image to the flash drive as follows:

1. 1.  Double-click on the InstallESD.dmg file to mount it on your Desktop.
   2. Open Disk Utility.
   3. Select the USB flash drive from the left side list.
   4. Click on the Restore tab in the Disk Utility main window.
   5. Select the USB flash drive volume from the left side list and drag it to the Destination entry field.
   6. Drag the mounted disc icon from the Desktop into the Source entry field.
   7. Double-check you got it right, then click on the Restore button.

When the clone is completed you have a fully bootable installer that you can use without having to re-download Mountain/Lion.