My recommendation is to get two dedicated Time Machine disks, in addition to the drive you have. Time Machine can backup to multiple disks. Then keep one at an offsite location, such as a relative's house or bank safe deposit box. Swap them every week or month depending on how much you are willing to lose. Because of the swapping I don't store data on the Time Machine disk, but if you choose to only keep one backup you can do this on a separate partition.
If you do it my way you won't need to have LightRoom create two copies, which I find to be very confusing, since TimeMachine will backup to a second and third disk.