There's a generic commadline tool for working a tape changer : mtx
(pacjkage name is also mtx)
in short, your tape changer should be known to you OS as a device (you'll have to find out which device name it is lnown as),
and then you use mtx to drive the robot, and mt to work with the LTO tape itself.
for backups, you need a program that can write to e device (rather than a filesystem) - eg. tar
It wouldn't surprise me if backup solutions like Amanda and Bacula can encapsulate all that, but maybe it helps if you know what you're looking for.
Here are some snippets from a backup script that uses an LTO robot : maybe you can see if something similar works with yours
those are the basics, 'man mtx' explains lots more
# slots - the slot in your tape magazine. You may want some logic to decide on what slot the tape comes from in stead of a hard number
# and you can store the tape in a different slot than where it came from
# show robot status
mtx -f $taperobot status
# load tape
mtx -f $taperobot load $slot_from 0
# do backup
tar c $tar_opts -f $tapedevice *
# unload tape
mt -f $tapedevice rewind ;# maybe not needed for LTO?
mtx -f $taperobot unload $slot_to 0
for remote backups : the easiest is probably to mount the backup source on the machine the tape device is attached to
you can also do it the other way around, i.e. send a backup to a "remote" tape (but the problem with that is that you also have to remotely control your robot for loading and unloading tapes)