iMac reinstallation

What version of macOS was on the iMac that you erased and what version of macOS will be installed with the installer you are using?

You don't use the "Restore" feature in Disk Utility to reinstall macOS. After properly erasing the drive you want to select the "Reinstall macOS" option. Depending on the old OS used and the OS being installed will affect how you actually prepare the drive plus Disk Utility has changed over the years which also affects the process somewhat as well.

In the mean time here is an Apple article for using Internet Recovery Mode, but the instructions for preparing the drive unfortunately assume you are installing a current OS and do not take into account older versions of macOS.

What is the exact model of your iMac and what is the version of macOS you are attempting to install plus what version of macOS was last installed on this Mac? You can get the exact model of the Mac by entering your serial number here:

https://checkcoverage.apple.com/

This information is important for us to know in order to provide the most specific instructions.

When booting to the macOS Lion installer do you see the physical drive listed on the left pane of Disk Utility? It should be the top most item which is usually named for the make & model of the internal drive. If you are trying to install macOS 10.6 to 10.10, then you need to partition and format the physical drive using the instructions in this article:

https://www.owcdigital.com/assets/support/support-formatting-and-migration/Mac_Formatting_6-10.pdf

In theory you should be able to boot into Internet Recovery Mode using Command + Option + R. Unfortunately Apple neglects to provide details on whether this works for any Mac or any OS although I thought I saw an Apple article at one time which mentioned this was the proper way to reinstall macOS Lion when selling the Mac so that macOS was not tied to your AppleID for the new owner.

If you have access to another Mac which is able to run macOS 10.11 or 10.13, then you can create a bootable macOS USB drive for the respective OS using the instructions in this Apple article:

How to create a bootable installer for macOS - Apple Support

To see which computers and versions of macOS are compatible you can check out this article:

https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

FYI, if you end up installing macOS 10.12+, then the instructions to prepare the physical drive are different. You would need to select the physical drive and the "Erase" tab in Disk Utility. The physical drive is hidden by default in Disk Utility beginning with macOS 10.13 so it may require clicking "View" within Disk Utility and selecting "Show All Devices" so that the physical drive appears on the left pane of Disk Utility.

A 2009 is way too old to access Internet Recovery.