GParted doesn't support LVM at all (unless this has changed recently?). You'll need to use the command line tools.
First, if you're booting from some rescue media, ensure that the volume group involved is active. The sequence will be something like
cryptsetup luksOpen /dev/sda2 encrypted
vgchange -ay /dev/mapper/my_volume_group
lvchange -ay /dev/mapper/my_volume_group-root /dev/mapper/my_volume_group-home
Then shrink the filesystem of the home volume. Use the right tool depending on the filesystem, e.g.
resize2fs for ext2/ext3/ext4,
resize_reiserfs for ReiserFS, …
Then resize the logical volumes, first shrinking
home to make room, then expanding
root to use the available space. Check the documentation for the units you can use with
lvreduce -L NEWSIZE /dev/mapper/my_volume_group-home
Finally extend the filesystem of the root volume.