LaCie successfully backed up computer with Time machine, now it won't.

<< Now the info about the drive says read only and I can't use time machine. >>

A working drive that spontaneously becomes Read Only can be an indication that the drive has developed a data problem that precludes Mounting the drive.

Launch Disk Utility, set the tiny View menu to 'show all devices'

and DiskRepair/FirstAid on each of these in order:

• the physical device

• the container-disk

• each Volume.

That you were able to complete one backup suggest the format was just fine.

"My La Cie rugged external hard drive (5T) backed up my Macbook Pro (2021, M1 ) computer completely. using Time Machine. Now the info about the drive says read only and I can't use time machine. This makes no sense to me. It's possible, I forgot to partition the drive when I got it, but then how did it back up my Mac? Since it did back it up via Time Machine, why won't it now?[...]"

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Time Machine Backing Up being Read Only:

A. Start Here: If a Time Machine Backup fails on Mac - Apple Support

B. Use First Aid in Disk Utility:

Se if you can fix the sectors on the drive, as they need to be parallel --not perpendicular. First Aid is intended to fix this. To do so: Open Disk Utility > Select: the Drive (on the left pane) > Click: First Aid > Let it Complete. If a Time Machine backup fails on Mac - Apple Support

C. Image Type:

Use AFPS: IF you chose APFS (Enterprise), then that means it is encrypted, and therefore, there is a password. If you did not create it as APFS, but rather of another type, it may work. See here: File System Formats Available in Disk Utility on Mac - Apple Support

D. Empty This by Formatting:

If you did not format it, then that is what you should have done. Being 5TB, it might take a few seconds to quite a lot of time.

E. Do NOT Partitions this:

When creating Time Machine Backups, partitions are not ideal. You should use it as one partition.