Hi there mlr99,
From what you describe it sounds like you are trying to install Lion on your newly installed HDD replacement but its not showing as a disk when you try to actually install Mac OS X. That indicates to me that the drive has not yet been formatted as Mac OS Extended Journaled, so it is not ready for Lion to install onto it. This section of the following article will help you get that drive erased and formatted properly so you can continue with the installation:
Or, you can boot your system from the original Mac OS X installation CD and run Disk Utility from the Installation menu. Your start-up disk is automatically verified and repaired (if necessary) during the boot procedure, so you really don’t need to worry about checking the start-up disk.
Thank you for using Apple Support Communities.
By default, your Mac starts up from its built-in hard disk, but a startup disk can be any storage device that contains an operating system compatible with your Mac. For example, if you install macOS on an internal or external drive, your Mac can recognize that drive as a startup disk. You can then follow the steps in this article to start up from it.
When you use Startup Disk preferences to select a startup disk, your Mac starts up from that disk until you choose a different one.
If you see a message that your security settings do not allow this Mac to use an external startup disk, check the External Boot setting in Startup Security Utility.
When you use Startup Manager to select a startup disk, your Mac starts up from that disk once, then returns to using the disk selected in Startup Disk preferences.
If your Mac is using OS X Lion 10.7.3 or later, you can also use this method to start up from your Time Machine backup disk. Startup Manager identifies your Time Machine backup as ”EFI Boot.”
Check for these possibilities if you can't see your disk in Startup Disk preferences or Startup Manager, or your Mac won't start up from it.
Make sure that your startup disk is using a version of macOS that is compatible with your Mac. If in doubt, use the same Mac to reinstall macOS on that disk.
To start up from an external disk with macOS Catalina 10.15 or later, the disk must connect via USB-A, USB-C, or Thunderbolt, not FireWire.
If you're using a Mac that has the Apple T2 Security Chip, check the settings in Startup Security Utility. These settings determine whether your Mac can start up from another disk.
If you're in Startup Manager and can't see a third-party startup disk, the startup disk could be using Option ROM firmware. To enhance system security, Mac computers with up-to-date software don’t show devices that use Option ROM firmware until you load their firmware. To do that, press Option-Shift-Command-Period while in Startup Manager. If your startup disk appears, do that each time you want to start up from it or from another disk connected to it.
If you're using a firmware password, the ability to load Option ROM firmware is disabled as an additional security protection.