You can copy the files to access.ces.school.edu and then transfer them to the other host.
Or you can ssh to access.ces.school.edu and from there scp user@lab:~/src user@home:~/dst
but to do that you need to setup a pub_key private_key authentication between your host at home and your Debian box. To do that:
1. At home box:
$ ssh-keygen -t dsa
2. At gateway access.ces.school.edu
$ scp user@home:~/.ssh/id_dsa.pub
$ scp ~/id_dsa.pub firstname.lastname@example.org
3. At a.ces.school.edu
$ cat ~/id_dsa.pub >> ~/.ssh/authorized_keys
$ chmod 700 ~/.ssh/authorized_keys
$ chmod 755 ~/.ssh
You might need to transfer the signature of both hosts on each other, I am not sure about this step cause I don't have same setup to try. but you got the idea.
If the above steps where successful you can from you lab just do ssh access.ces.school.edu 'scp user@lab:~/src user@home:~/dst'
Again I don't have the setup to try that, so If It's successful with you please let me know.