How do I set up an external drive for Lightroom classic on MacBook Pro

Yes, you can use the same 4T external drive with Time Machine and your Lightroom Classic files. You will need to create an additional APFS volume on that drive so that TM has one volume to itself. Apple provides guidance for using external disks with TM here: Types of disks you can use with Time Machine on Mac - Apple Support

Most veteran users will tell you that sharing a backup drive with normal file storage is not the best practice. When (not if) the drive fails it will take not only your backup but your saved files away with it. You'd be wise to buy a second external drive for TM to use exclusively.

Storing both active data and backups on the same device can be — arguably is — unwise. Not when one failure clobbers all.

Usual external sizing for Time Machine is two to three times the aggregate size of the protected storage, as this provides both some depth of backups, and can also deal with large-file churn.

if you have the budget for it, a NAS with Time Machine server support works well for laptop backups, and also for shared storage. That means you don’t have to connect the devices, and the backups will run when connected to the same Wi-Fi network as of the NAS.

I’d also suggest updating macOS to current, and using a second drive.