Cannot Install Mac OS X Lion

I just recently assisted another user and they were able to reinstall macOS 10.7 Lion through Internet Recovery Mode. They had to make sure the date & time were current first. Assuming the Mac has already been erased, then you will need to launch the Terminal app from the Utilities menu on the menu bar and issue the following command to configure the time through Apple's network time servers (macOS 10.13 & earlier):

ntpdate  -vu  time.apple.com

I would first try booting into Internet Recovery Mode using Command + Option + R to attempt to access the macOS 10.13 online installer assuming that macOS 10.12.4+ had previously been installed at some point in the past. If not, then it will just default to booting to the macOS 10.7 Lion online installer which also bypasses a need to confirm an AppleID purchase of Lion. Make sure to configure the system date & time to be current. It seems Apple got the online installers fixed as well as updated their security certificates since the other user I was assisting was successful. Unfortunately no matter the keys used for booting into recovery mode, some Macs will just boot to the online installer for the OS which originally shipped with the Mac from the factory.

Unfortunately you cannot make a bootable macOS 10.7 Lion installer from the downloaded .dmg file. That file only an archive bundle which contains a .pkg file which must be run to extract the real Lion installer into the Applications folder. This requires a Mac compatible with Lion (generally 2007 to 2011) as the .pkg file will not run on anything else. Even then, I don't believe their is any built-in command to automatically create a bootable macOS 10.7 Lion USB installer, although it may be possible to manually make one, but I have not seen any recent instructions to do so with the recent version of the installer. I doubt the older instructions from 2011 would work on the latest version of the Lion installer even after it has been extracted to the Applications folder.

It would be much easier to create a bootable macOS 10.11 or 10.13 USB installer since instructions are available from Apple:

Create a bootable installer - Apple Support

This would generally require a Mac from:

• 2007 to 2015 for macOS 10.11
• Late-2009 to mid-2018 for macOS 10.13

I think Internet Recovery Mode using Command + Option + R is the easiest & best option at the moment unless you can find someone with a Mac from 2007 to mid-2018.

I never used Time Machine, but were the older backups able to be used to restore a Mac completely including the ability to restore the OS as well? That might be worth trying if you have a TM backup. I know later TM backups no longer backup the OS system files.

OK, thanks, do you really need Lion?

Start up from macOS Recovery

To start up from macOS utilitRecovery, turn on your Mac and immediately press and hold one of the following combinations on your keyboard. Command-R is generally recommended, especially if you never installed macOS Sierra 10.12.4 or later… How to reinstall macOS - Apple Support

Command (⌘)-R

Install the latest macOS that was installed on your Mac.

Option-⌘-R

Upgrade to the latest macOS compatible with your Mac.

Shift-Option-⌘-R

Install the macOS that came with your Mac, or the closest version still available.

2. Decide whether to erase (format) your disk

If you need to erase your disk before installing macOS, select Disk Utility from the Utilities window, then click Continue. You probably don't need to erase, unless you're selling or giving away your Mac or have an issue that requires you to erase. Learn more about when and how to erase.

3. Install macOS

After starting up from macOS Recovery, follow these steps to install macOS:

1. Choose Reinstall macOS (or Reinstall OS X) from the Utilities window.
2. Click Continue, then follow the onscreen instructions to choose your disk and begin installation.
3. If the installer asks to unlock your disk, enter the password you use to log in to your Mac. If it doesn't see your disk, or it says that it can't install on your computer or volume, you might need to erase your disk. 

1. Please allow installation to complete without putting your Mac to sleep or closing its lid. During installation, your Mac might restart and show a progress bar several times, and the screen might be empty for minutes at a time.

If your Mac restarts to a setup assistant, but you're selling or giving it away, press Command-Q to quit the assistant without completing setup. Then click Shut Down. When the new owner starts up the Mac, they can use their own information to complete setup.

If you never installed macOS Sierra 10.12.4

If macOS Sierra 10.12.4 or later was never installed on your Mac, macOS Recovery works differently:

• Command-R is still the recommended way to start up from macOS Recovery. This combination makes sure that the installation isn't associated with your Apple ID, which is important if you're selling or giving away your Mac.
• Option-Command-R installs the macOS that came with your Mac, or the closest version still available.
• Shift-Option-Command-R isn't available.

How to reinstall macOS - Apple Support 

Of course you may need to make a USB installer...

Create a bootable installer for macOS - Apple Support...

Create a bootable installer - Apple Support

It will not work in the .DMG state...

Safari downloads the following installer as a disk image named InstallMacOSX.dmg. Open the disk image, then open the .pkg installer inside the disk image. It installs an app named Install Mac OS X Lion. Open that app from your Applications folder to begin installing the operating system.

Please allow installation to complete without putting your Mac to sleep or closing its lid. During installation, it might restart and show a progress bar or blank screen several times. You might find it easiest to begin installation in the evening so that it can complete overnight, if needed.

How to install Mac OS X Lion 10.7 - Apple Community

• Insert a USB key with OS X install into Mac (or install disc)
• Power up and hold the Option key down as soon as you hear the startup chime.
• Choose OS X to install
• Once booted into recovery, choose Utilities from the menu and then Terminal.
• Type date into Terminal and hit enter; this displays the date; if it is not the current date, you need to go to the next step.
• Type date into Terminal followed by today’s date in this format [month][day][hour][minute][year] so today is July 11, 2016, 2:15 that would be date 0711141516 then press enter. Of course, your date and time will vary.
• Rerun the first command in Terminal date and press enter; the date should now be fixed.

At this point, you should now be able to continue your reinstall of OS X on your Mac, and the installation error should no longer appear. For whatever reason, the system date matters when installing the OS on your Mac. So if you get that error, don’t panic and think your Mac is toast, try this fix first, and you should be golden.

https://techaeris.com/2016/07/11/change-system-date-os-x-terminal/#google_vignette

Date and time parameter using the format [MM][DD][HH][MM][YY]. 

Example: April 15, 2022, 11:00 am would be 0415110022, so now would be...

0106161424

Note: The time uses a 24-hour format

Hey I have a mac mini 2010 that requires the Mac OS X Lion Im trying to sell it so I already deleted the disk and formated to Mac OS Extended (Journaled) and also put the date as if is 2018 but when i tried to download the Lion the same problem occurs a big number and the 0 seconds

Once mounted you need to copy the Install Mac OS X Lion.app to YUH2...

Manage files in Terminal on Mac - Apple Support

cp /Volumes/YUH1/InstallMacOSX.app /Volumes/YUH2

Can you use the second USB drive to Restore the Lion DMG to it as Install Mac OS X Lion.app ???

It'd wipe out anything on the 2nd drive.