Could you please confirm which version of Lightroom did your son purchase?
It depends whether he purchased Windows version or Mac or multi-platform.
If he purchased multi-platform version, then you can go for download and use the same serial key to activate it otherwise, you might have to go for platform swap or a new purchase depending upon the version as only current version platform swap is supported.
You need to go online at Adobe ID and sign in with the email address through which Lightroom was purchased to get the product details.
Let us know if you have further queries.
I will ask my son and my husband to help me figure this out. I haven’t actually even used it once yet.