When trying to install Mac OS lion it says this Item Temporarily unavailable this is in recovery mode

Okay, your (now hidden) serial number indicates this is a MacBook Pro (13-inch, Early 2011).

That’ll run High Sierra.

With no backups, there’s not a whole lot of reason to use an older OS X release, either.

Using another Mac, download High Sierra there, and built a bootable installer.

Using Safari on the other Mac, here’s the High Sierra download:

https://itunes.apple.com/us/app/macos-high-sierra/id1246284741?ls=1&mt=12

Once you have the installer downloaded on a different Mac, here is how to build a bootable installer:

How to create a bootable installer for macOS - Apple Support

Transfer the installer over to the MacBook Pro, and boot and install from that.

I might try using Disk Utility from within Recovery or from within the bootable installer to try to get a backup of the storage contents to external storage, if the target has not already been wiped.

This Mac has removable internal storage, so a potentially-failing hard disk can be replaced, and there’s room for an SSD upgrade for better performance should you be planning to keep this MacBook Pro for a while longer. Failing hard disks can show as slower performance and beachballs (“system wait cursor”), and as crashes and corruptions and hangs. That’ll generally orogress into data loss.

Apple hardware Test can find some (but far from all) errors: How to use Apple Hardware Test on your Mac - Apple Support

Usual underlying reason for a factory reset that gets somebody this ancient is failing hardware.

Often a failing hard disk.

Which Mac is involved here, both Mac model and year?

What macOS version was this Mac running, prior to this adventure?

Do you have another Mac handy?

Do you have backups?

Look at the bottom, or at the back, or underneath the foot on an iMac, and find the model code. Please post that.

Why I ask?

Details on the type of Mac—iMac, MacBook, etc—and the year matter, and ~2010 was one of the cut-over years; some 2009 to late 2010 supports High Sierra, some only gets El Capitan. Knowing those details can avoid writing and avoid reading long and confusing posting with if-you-have-this-then-that and if-you-have-that-then-this. And I can point to tailored info, such as how to identify your specific iMac.

Details here matter.

If you're getting Lion 10.7 during Recovery, you probably weren’t running Snow Leopard 10.6.

Okay... Three questions...

Which Mac is involved here, both Mac model and year? If you are not sure of that, post the model code as mentioned above.

Do you have another Mac handy? That can be useful for building recovery tools.

Do you have backups? If not, that simplifies the reinstallation. If you do have backups, those need to from the same or an earlier macOS version.