The following note shows how to use Zypper to do a live distribution upgrade of openSUSE Leap 15.5 to openSUSE Leap 15.6.

thounchey3:~ # cat /etc/os-release
NAME="openSUSE Leap"
VERSION="15.5"
ID="opensuse-leap"
ID_LIKE="suse opensuse"
VERSION_ID="15.5"
PRETTY_NAME="openSUSE Leap 15.5"
ANSI_COLOR="0;32"
CPE_NAME="cpe:/o:opensuse:leap:15.5"
BUG_REPORT_URL="https://bugs.opensuse.org"
HOME_URL="https://www.opensuse.org/"
DOCUMENTATION_URL="https://en.opensuse.org/Portal:Leap"
LOGO="distributor-logo-Leap"

Check for the 3 required repositories, ensure they are enabled.`

thounchey3:~ # zypper lr -u
Repository priorities are without effect. All enabled repositories share the same priority.

#  | Alias                       | Name                                                                                        | Enabled | GPG Check | Refresh | URI
---+-----------------------------+---------------------------------------------------------------------------------------------+---------+-----------+---------+------------------------------------------------------------------------
 1 | repo-backports-debug-update | Update repository with updates for openSUSE Leap debuginfo packages from openSUSE Backports | No      | ----      | ----    | http://download.opensuse.org/update/leap/15.5/backports_debug/
 2 | repo-backports-update       | Update repository of openSUSE Backports                                                     | Yes     | (r ) Yes  | Yes     | http://download.opensuse.org/update/leap/15.5/backports/
 3 | repo-debug                  | Debug Repository                                                                            | No      | ----      | ----    | http://download.opensuse.org/debug/distribution/leap/15.5/repo/oss/
 4 | repo-debug-non-oss          | Debug Repository (Non-OSS)                                                                  | No      | ----      | ----    | http://download.opensuse.org/debug/distribution/leap/15.5/repo/non-oss/
 5 | repo-debug-update           | Update Repository (Debug)                                                                   | No      | ----      | ----    | http://download.opensuse.org/debug/update/leap/15.5/oss/
 6 | repo-debug-update-non-oss   | Update Repository (Debug, Non-OSS)                                                          | No      | ----      | ----    | http://download.opensuse.org/debug/update/leap/15.5/non-oss/
 7 | repo-non-oss                | Non-OSS Repository                                                                          | Yes     | (r ) Yes  | Yes     | http://download.opensuse.org/distribution/leap/15.5/repo/non-oss/
 8 | repo-openh264               | Open H.264 Codec (openSUSE Leap)                                                            | Yes     | (r ) Yes  | Yes     | http://codecs.opensuse.org/openh264/openSUSE_Leap/
 9 | repo-oss                    | Main Repository                                                                             | Yes     | (r ) Yes  | Yes     | http://download.opensuse.org/distribution/leap/15.5/repo/oss/
10 | repo-sle-debug-update       | Update repository with debuginfo for updates from SUSE Linux Enterprise 15                  | No      | ----      | ----    | http://download.opensuse.org/debug/update/leap/15.5/sle/
11 | repo-sle-update             | Update repository with updates from SUSE Linux Enterprise 15                                | Yes     | (r ) Yes  | Yes     | http://download.opensuse.org/update/leap/15.5/sle/
12 | repo-source                 | Source Repository                                                                           | No      | ----      | ----    | http://download.opensuse.org/source/distribution/leap/15.5/repo/oss/
13 | repo-update                 | Main Update Repository                                                                      | Yes     | (r ) Yes  | Yes     | http://download.opensuse.org/update/leap/15.5/oss/
14 | repo-update-non-oss         | Update Repository (Non-Oss)                                                                 | Yes     | (r ) Yes  | Yes     | http://download.opensuse.org/update/leap/15.5/non-oss/

thounchey3:~ # zypper refresh
Repository 'Update repository of openSUSE Backports' is up to date.
Repository 'Non-OSS Repository' is up to date.
Repository 'Open H.264 Codec (openSUSE Leap)' is up to date.
Repository 'Main Repository' is up to date.
Repository 'Update repository with updates from SUSE Linux Enterprise 15' is up to date.
Repository 'Main Update Repository' is up to date.
Repository 'Update Repository (Non-Oss)' is up to date.
All repositories have been refreshed.

thounchey3:~ # zypper update
Loading repository data...
Reading installed packages...
Nothing to do.
thounchey3:~ # grep baseurl /etc/zypp/repos.d/*.repo | grep -v releasever                                                     [1321/1321]
/etc/zypp/repos.d/repo-openh264.repo:baseurl=http://codecs.opensuse.org/openh264/openSUSE_Leap/
thounchey3:~ # zypper --releasever=15.6 refresh
Warning: Enforced setting: $releasever=15.6
Retrieving repository 'Update repository of openSUSE Backports' metadata ..........................................................[done]
Building repository 'Update repository of openSUSE Backports' cache ...............................................................[done]
Retrieving repository 'Non-OSS Repository' metadata ...............................................................................[done]
Building repository 'Non-OSS Repository' cache ....................................................................................[done]
Repository 'Open H.264 Codec (openSUSE Leap)' is up to date.                                                                             Retrieving repository 'Main Repository' metadata ..................................................................................[done]
Building repository 'Main Repository' cache .......................................................................................[done]
Retrieving repository 'Update repository with updates from SUSE Linux Enterprise 15' metadata .....................................[done]
Building repository 'Update repository with updates from SUSE Linux Enterprise 15' cache ..........................................[done]
Retrieving repository 'Main Update Repository' metadata ...........................................................................[done]
Building repository 'Main Update Repository' cache ................................................................................[done]
Retrieving repository 'Update Repository (Non-Oss)' metadata ......................................................................[done]
Building repository 'Update Repository (Non-Oss)' cache ...........................................................................[done]
All repositories have been refreshed.
thounchey3:~ # zypper --releasever=15.6 dup --download-in-advance
Warning: Enforced setting: $releasever=15.6
Loading repository data...
Reading installed packages...
Warning: You are about to do a distribution upgrade with all enabled repositories. Make sure these repositories are compatible before you
 continue. See 'man zypper' for more information about this command.
Computing distribution upgrade...

The following 163 packages are going to be upgraded:
  ansible apparmor-abstractions apparmor-parser apparmor-profiles bind-utils branding-openSUSE cracklib cracklib-dict-small
  crypto-policies curl dracut dracut-mkinitrd-deprecated e2fsprogs fipscheck firewalld fish gettext-runtime gio-branding-openSUSE
  girepository-1_0 git git-core glib2-tools glibc glibc-devel glibc-locale glibc-locale-base gpg2 grub2 grub2-branding-openSUSE
  grub2-i386-pc grub2-x86_64-efi haveged htop hwloc-data ipset jeos-firstboot kmod krb5 less libapparmor1 libargon2-1 libaugeas0
  libblkid1 libbsd0 libcom_err2 libcontainers-common libcontainers-default-policy libcrack2 libcryptsetup12 libcurl4 libdevmapper1_03
  libext2fs2 libfdisk1 libfido2-1 libfido2-udev libfipscheck1 libgcrypt20 libgio-2_0-0 libgirepository-1_0-1 libglib-2_0-0
...

...
dracut[I]: *** Stripping files ***
dracut[I]: *** Stripping files done ***
dracut[I]: *** Creating image file '/boot/initrd-6.4.0-150600.21-default' ***
dracut[I]: *** Creating initramfs image file '/boot/initrd-6.4.0-150600.21-default' done ***
Running post-transaction scripts ..................................................................................................[done]
There are running programs which still use files and libraries deleted or updated by recent upgrades. They should be restarted to benefit from the latest updates. Run 'zypper ps -s' to list these programs.

Since the last system boot core libraries or services have been updated.
Reboot is suggested to ensure that your system benefits from these updates.
reboot
❯ cat /etc/os-release
NAME="openSUSE Leap"
VERSION="15.6"
ID="opensuse-leap"
ID_LIKE="suse opensuse"
VERSION_ID="15.6"
PRETTY_NAME="openSUSE Leap 15.6"
ANSI_COLOR="0;32"
CPE_NAME="cpe:/o:opensuse:leap:15.6"
BUG_REPORT_URL="https://bugs.opensuse.org"
HOME_URL="https://www.opensuse.org/"
DOCUMENTATION_URL="https://en.opensuse.org/Portal:Leap"
LOGO="distributor-logo-Leap"

Reference: