/usr/share/initramfs-tools/ is in ltsp-client-core 5.5.1-1ubuntu2.
This file is owned by root:root, with mode 0o755.
..
/usr/share/initramfs-tools/hooks/
/usr/share/initramfs-tools/hooks/ltsp
/usr/share/initramfs-tools/hooks/udhcp
/usr/share/initramfs-tools/scripts/
/usr/share/initramfs-tools/scripts/init-bottom/
/usr/share/initramfs-tools/scripts/init-bottom/ltsp
/usr/share/initramfs-tools/scripts/init-premount/
/usr/share/initramfs-tools/scripts/init-premount/udhcp
/usr/share/initramfs-tools/scripts/local-top/
/usr/share/initramfs-tools/scripts/local-top/aoe_ltsp
/usr/share/initramfs-tools/scripts/local-top/nbd_ltsp
/usr/share/initramfs-tools/scripts/nfs-bottom/
/usr/share/initramfs-tools/scripts/nfs-bottom/ltsploop