Updating from lion to El Capitan

What model / year of Mac do you have exactly?

Click here ➜ OS X El Capitan - Technical Specifications - Apple Support

If you have a compatible model, you will need to download the macOS installer from Apple's website and run it on your Mac.

click here ➜ How to download and install macOS - Apple Support

The browsers running on Lion probably won't be able to handle the https security on this forum or on the "How to download and install macOS" page. There was a major change to https security, and I don't think that versions of Mac OS X prior to El Capitan got updates for it.

So, if your Mac is compatible with El Capitan, you may want to use a modern Mac or PC to download the .DMG file containing the El Capitan installer, putting it onto a USB flash drive. Then you can transfer the flash drive to the old Mac and copy the .DMG file onto it. Finally you can use Lion to open (mount) the .DMG and run the installer.

Another alternative would be to copy the link for the El Capitan installer. that's a http link, so even Lion should be able to handle it. But I believe it's a somewhat inconvenient link to try to type by hand …

Should be able to cut-and-paste it:

http://updates-http.cdn-apple.com/2019/cert/061-41424-20191024-218af9ec-cf50-4516-9011-228c78eda3d2/InstallMacOSX.dmg