How do I access my old files from an old Macbook HDD with Lubuntu?
This is probably due to your FS type and your old disk which is probably HFS+.
You need to add extra packages to read it.
Try this link: https://askubuntu.com/questions/332315/how-to-read-and-write-hfs-journaled-external-hdd-in-ubuntu-without-access-to-os
Here's the copy paste of the answer :

First, make sure that you have hfsprogs installed. Example installation command:
sudo apt-get install hfsprogs

Next, mount or remount the HFS+ drive; commands need to be as follows:
sudo mount -t hfsplus -o force,rw /dev/sdXY /media/mntpoint

or
sudo mount -t hfsplus -o remount,force,rw /mount/point

Finally, if the drive was improperly unmounted or has otherwise become partially corrupted run fsck.hfsplus ... as such:
sudo fsck.hfsplus -f /dev/sdXY