Is it possible to on-line shrink a EXT4 volume with LVM?

yes..

you can use --resizefs flag to lvreduce command.

lvreduce --size -2G  --resizefs /dev/<volumegroup-name>/<logical-volume-name>

Command Example

If the case is remote server without console, you can shrink filesystem using initramfs while rebooting. You need to add resize2fs to initramfs and run it before mounting root.

Debian/Ubuntu example:

/etc/initramfs-tools/hooks/resizefs (executable):

#!/bin/sh

set -e

PREREQS=""

prereqs() { echo "$PREREQS"; }

case $1 in
    prereqs)
        prereqs
        exit 0
    ;;
esac

. /usr/share/initramfs-tools/hook-functions

copy_exec /sbin/e2fsck
copy_exec /sbin/resize2fs
    
exit 0

/etc/initramfs-tools/scripts/local-premount/resizefs (executable)

#!/bin/sh

set -e

PREREQS=""

prereqs() { echo "$PREREQS"; }

case "$1" in
    prereqs)
        prereqs
        exit 0
    ;;
esac

# simple device example
/sbin/e2fsck -yf /dev/sda1
/sbin/resize2fs /dev/sda1 5G # see size info below
/sbin/e2fsck -yf /dev/sda1

# complex device example
# activate md-raid containing FS/PV
#/sbin/mdadm -A /dev/md0
# activate VG containing FS
#/sbin/lvm vgchange -ay vg0
# resize
#/sbin/e2fsck -yf /dev/vg0/root # or /dev/md0
#/sbin/resize2fs /dev/vg0/root 5G
#/sbin/e2fsck -yf /dev/vg0/root

Now run update-initramfs -u -k kernel-name to update initramfs for the kernel kernel-name which is set as default in your bootloader (grub). In case of boot failure - you can boot with another unmodified healthy kernel/initramfs. Or you can use all to update all kernels, but then you have no way back.

Check that you do not have any tools in your system that grow filesystem automatically (e.g. cloud-init - comment resizefs in /etc/cloud/cloud.cfg).

Reboot. Check filesystem size. Remove initramfs scripts and run update-intiramfs -u -k kernel-name again.

Now you can shrink underlying device with parted resizepart / mdadm --grow --size= / lvresize -L. The size of the device should be bigger then the size of filesystem from the scripts. The simplest way to make no mistakes: if planned device size - 6G. set fs size in the script to 5G. after fs is resized - resize device to 6G, then grow fs to maximum online with resize2fs /dev/sda1. Now your fs fits perfectly in your device.

For dracut (Fedora,CentOS) use the same logic (/usr/lib/dracut/modules.d).

This is very usefull for crypting or moving rootfs, with no free space available for the new partition.

Yes, you can shrink/move/grow a root partition without any reboots (nor livecd, nor usbkey): consult this answer. It's very well written and easy to follow, although quite long and a little risky.

resize2fs can't shrink online ext4 partitions. This limitation, when applied on the root partition may lead you to think you can't avoid rebooting the host to allow shrinking the root partition, which might be something you want to avoid. The linked process will allow you to umount the root partition without any reboots. So in this light it is not strictly speaking online resizing in regards to the mounted state of the partition, however it remains an online resizing in regards to the network online status or reachability of the host.

Of course, if you only want to grow your ext4 partition, you should stick to the conventional working resize2fs solutions.

The general solution I've linked will work on any type of dedicated or VPS solution for instance.

TLDR; this solution implies to pivot_root to tmpfs so you can umount safely your root partition live and fiddle with it. Once done, you'll pivot_root back on your new root partition.

This allows pretty much any manipulation on the root file system (move it, change filesystem, changing it's physical device...).

I have personally used this, and it works very well on debian system also, but the guide was initially written in 2007 for redhat, the answer I've linked was updated for CentOS7. It's highly probable that it'll work on your OpenSUSE, although probably with some adaptation.

As the message said, you can only grow an ext4 filesystem on-line. If you want to shrink it, you will need to unmount it first.

According to the ext4 filesystem maintainer, Ted Ts'o:

Sorry, on-line shrinking is not supported.