Unable to upgrade from os x lion to catealina

Download and install macOS 10.11 El Capitan first (read the instructions carefully since there are multiple steps involved to extract & run the installer):

How to download macOS - Apple Support

You first need to have macOS 10.9+ installed before you can use the Catalina installer.

macOS Catalina - Technical Specifications

I highly recommend creating a bootable macOS 10.11 USB installer so you have more options in case something goes wrong.

Create a bootable installer for macOS - Apple Support

If this laptop at one time had macOS 10.12.6+ installed, then you can instead boot into Internet Recovery Mode using Command + Option + R to access the online macOS 10.15 Catalina installer (theoretically since some times it may only boot to the Lion/Mountain Lion installer instead).

If you already have a macOS installer app in the Applications folder, then first delete it and empty the Trash in case the existing file has an issue.

Are you getting the "Download Again" error when attempting to install macOS 10.11 while booted into macOS 10.7? If so, then try changing the date to some time in 2017 and see if it works. I know that Apple gives cryptic misleading errors which some times is just referring to an outdated certificate, so moving the system date earlier will make the installer think the certificate is still valid.

Big Sur and Catalina are irrelevant if you are currently running macOS 10.7 because those installers require you are already running at later version of macOS. Plus if this laptop never had a later version of macOS installed, then you may need to install one or two intermediate versions first.

Keep in mind I cannot see what is happening, so knowing exact details and error messages, plus when they occur are very important.