How to update from Mac OS X (lion)

A 2012 21.5" iMac can run Catalina 10.15. A 2011 21.5" iMac can run up to High Sierra. So first you have to determine what you own, then click the Apple Symbol in the upper left of the display and I believe you will find a link that allows you to update.

However to be 150% honest with you, Both 2011 and 2012 iMacs are quite antiquated devices meaning they are obsolete (cannot run current versions of Mac OS) and are classified as Vintage (meaning parts are largely unavailable) so if I was in your shoes, I would seriously consider replacing with a more up-to-date machine and simply use one of Apple's free recycling services to get rid of the old Mac.

ALSO and this is critical, you indicated the computer was passed down to you. Was the computer prepared for you by the original owner per Apple's instructions in What to do before you sell, give away, or trade in your Mac? If you do not know or the answer is no then you will never get this thing to run correctly because it will always be associated with the old owner. We see similar posts to yours almost daily where people somehow get a used Mac and it wasn't prepared correctly for them. Basically they are simply left with a boat anchor at that point.

In order to help, we need the model year of your 21.5 iMac.

Have the original owner set it up per the directions in the link provided, then you can start over and have the computer associated to you and update Mac OS as far as it has the ability to.