Apple remote’s have unique identifiers (well, there are 256 unique codes, so about as unique as a door key…) that allow the receiver to “pair” with a particular remote.
We actually had to go to some trouble to create profiles for the Apple remote’s that would work with all Apple remote’s… 
Have a look at the file /etc/lirc/apple-silver-A1294-lircd.conf or /etc/lirc/apple-white-A1156-lircd.conf depending on which remote you have.
(You can also see these files here: osmc/package/remote-osmc/files/etc/lirc at master · osmc/osmc · GitHub )
The ignore_mask line is the one that ignores the unique code of each remote, so without this line it will then take notice of the pre_data value which varies from remote to remote.
Unfortunately the only easy way I know to find out what the pre_data value should be for your particular remote is to learn it from scratch using irrecord, thus creating your own custom lircd.conf file.
That’s not as hard as it sounds. First you need to log in with SSH. Next you need to stop the lircd daemon from running (this will disable the remote in Kodi temporarily) using:
sudo systemctl stop lircd_helper@lirc0
Next run the irrecord program with the right options to create a new conf file:
irrecord -d /dev/lirc0 apple-white.conf
Then it’s just a matter of following the instructions to press buttons when it tells you and name the buttons - refer to the button naming in the original files and use the same names. (KEY_UP, KEY_OK and so on…)
Once that is finished restart lircd:
sudo systemctl start lircd_helper@lirc0
Now go into the remotes section in OSMC settings and use the browse option to browse to your custom conf file. In theory it should work and it will now only respond to this remote and not the other one you have - effectively it is paired. Then repeat the process on your other Pi with your other remote…