Can Logic Pro be purchased/acquired online for a MacBook already being used?

It's available through the "App Store". In the US App Store, it's here: Logic Pro X on the Mac App Store

You dont have to buy a new computer to purchase Logic online.

You can buy Logic for an Apple computer you own.

However, You should check the Logic Pro X site to confirm you have the right spec to install Logic, ie: RAM, OS etc

Hope that helps

One thing to note:

Logic can use a -lot- of hard drive space if you download all the additional content. The initial installation is 3-4 gigabytes, additional content can be 50-60 GB.