I hope I'm not missing something obvious here. The point of LVM is that you can use multiple partitions as one single file system. One of the useful points about this is that you can extend a file system onto any new partition (even spanning across disks).
So in your case you can just create a new partition in the allocated space, add this to your volume group and the extend your logical volume to use the extra space.
I'm afraid I don't have instructions on doing this with gparted but here's a relativly straight forward tutorial on how to expand an LVM by adding a partition.
https://www.systutorials.com/5621/extending-a-mounted-ext4-file-system-on-lvm-in-linux/
The simple version of the steps are:
- Create a new (un-formatted) partition (use
cfdisk
or fdisk
)
- Setup the partition as a an LVM physical volume
pvcreate
- Add the new physical volume to your volume group using
vgextend
- Extend the logical volume to use the extra space using
lvextend
- (If not done in step 4) resize the ext4 file system using
resize2fs
/home
.