Need to update my White MacBook from OS X Lion to the most recent

The model and year of your Mac will determine which macOS you can upgrade to,

read the following links.

https://support.apple.com/macos/mojave

How to upgrade to macOS High Sierra - Apple Support

How to upgrade to OS X El Capitan - Apple Support

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

macOS Catalina 10.15 was released recently, the latest version of macOS.

If you are considering upgrading to Catalina be warned that it does not support 32bit apps.

Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,

some updates may be free, some may be paid. Use this app to discover which apps you have

are 32bit, https://www.stclairsoft.com/Go64/. Once the list has been created you can then

contact the developers of the apps to see if they provide 64bit updates. 

How to upgrade to macOS Catalina – Apple Support

Oh for goodness sake, click on the Apple top left of your screen, click on About This Mac., that will give you information

on your Mac. If it is definitely from 2008, you can only upgrade to El Capitan.

There is a link in my earlier post,

How to upgrade to OS X El Capitan – Apple Support