In this situation, I recommend using disk utility to partition the larger drive such that one partition matches the size of the smaller drive. Then setup the partitions of the same size as a RAID1. You will end up with a mirrored partition of 1.5TB and another un-mirrored partition of 0.5TB based on your first example.
Same thing will work for a 2TB + 3TB drive, but the mirrored/un-mirrored partitions will be 2TB and 1TB, respectively. Brand won't matter and you can use disk utility to find the exact sizes.
Firstly, RAID shouldn't include your backups. Something catastrophic hitting one, will hit the other. Eg. fire, burglary, etc.
Ideally, you want to keep one set off site. Using the 2 disks you can keep one at a friends, and sync the up periodically. There are tools that allow you to do this. Alternatively, something like BackBlaze, Amazon Glacier, will give you huge or unlimited storage that is remote and protected.
Secondly, when setting up RAID you want to think about your priorities. Are you optimizing for speed, redundancy, etc.
I you want to have one unit in house, and one remote and periodically updated, you're probably better off with RAID5, which is a better mixture of redundancy and speed.
Finally, RAID won't allow you to upgrade disks singly.
Alternatively, using a something like Zevo's ZFS you can configure the Big5 as a JBOD and feed the disks into a ZFS RAIDZ. This will allow you to mix and match disk sizes, and upgrade over time. It will also keep better control of your disks, checksum all the data, and a host of other features.
Personally, I'm a big fan of the ZFS approach, as I think the performance and security are better than a plain RAID.
RAIDing using OSX software, on top of a RAID in the LaCie box is asking for some complex failure.
Best Answer
It is not possible and even if it were it would be a very bad idea.
RAID 1 is to protect from hardware failure, and as described in the Apple document Create a disk set using Disk Utility on Mac mentioned by @user3439894 in comments, requires multiple disks (not partitions).
Even if it were possible it would provide no protection against hardware failure (as both partitions are on the same disk) and in the case of a HDD would drastically reduce write performance as the disk arm would have to continuously jump back and forward between partitions.
While it may theoretically give some limited protection against bad blocks if you only have one disk you would be much better off making a a backup to another partition (which would protect you from accidental file deletion). Backup to another to another disk would protect you from disk failure and file loss while RAID 1 is only designed to protect from hardware failure.