When using a loop file for backing LVM, it is necessary to start losetup before LVM can start. This is easily done using systemd and putting it into startup. This example service unit uses Ubuntu 24.04

Create the file /etc/systemd/system/loops-setup.service

[Unit]
Description=Setup loopback devices

DefaultDependencies=no
Conflicts=umount.target

Requires=-.mount
Before=local-fs.target umount.target
After=-.mount

[Service]
ExecStart=/sbin/losetup /dev/loop0 /data-disk.img
ExecStop=/sbin/losetup -d /dev/loop0

RemainAfterExit=yes
Type=oneshot

[Install]
WantedBy=local-fs-pre.target

Add the service to startup and start it

systemctl enable --now loops-setup.service

losetup --list
NAME       SIZELIMIT OFFSET AUTOCLEAR RO BACK-FILE      DIO LOG-SEC
/dev/loop0         0      0         0  0 /data-disk.img   0     512