Ubuntu 22.04 bash one-liner to identify device backing a LUKS volume?

There might be a simpler and more efficient way to do this, but I was able to achieve what you want using lsblk, grep, and awk without needing root access.

tl;dr

pkname=$(lsblk -o MOUNTPOINT,PKNAME | grep "^/"[^[:alnum:]] | awk '{ print $2 }');pkname=$(lsblk -o PATH,PKNAME,KNAME | grep $pkname | awk -v val="$pkname" '$3 == val { print $2 }');lsblk -o PATH,KNAME | grep $pkname | awk '{ print $1 }';unset pkname

Let's break it down and use a test VM as an example, Ubuntu 22.04.3 Server. Start with the output of lsblk. As you can see, all the info you want is there. It shows the mountpoint and path up the tree to /dev/sda3. The challenge is how to parse this output to get the path /dev/sda3 from the mountpoint, /.

$ lsblk
NAME                        MAJ:MIN RM   SIZE RO TYPE  MOUNTPOINTS
loop0                         7:0    0  63.4M  1 loop  /snap/core20/1974
loop1                         7:1    0 111.9M  1 loop  /snap/lxd/24322
loop2                         7:2    0  53.3M  1 loop  /snap/snapd/19457
sda                           8:0    0    25G  0 disk  
├─sda1                        8:1    0     1M  0 part  
├─sda2                        8:2    0     2G  0 part  /boot
└─sda3                        8:3    0    23G  0 part  
  └─dm_crypt-0              253:0    0    23G  0 crypt 
    └─ubuntu--vg-ubuntu--lv 253:1    0    23G  0 lvm   /
sr0                          11:0    1  1024M  0 rom  

Fortunately, lsblk has an -o option that allows you to supply a list of columns to print. This displays additional info that can be parsed with grep and awk. Look at lsblk --help for a complete list. To start, I chose MOUNTPOINT and PKNAME, but I'll also be using PATH and KNAME later.

$ lsblk --help
--snip--
 KNAME  internal kernel device name
 PATH  path to the device node
--snip--
 MOUNTPOINT  where the device is mounted
--snip--
 PKNAME  internal parent kernel device name
--snip--

1. Find the PKNAME for mountpoint: /

The following line prints the MOUNTPOINT and PKNAME associated with / mountpoint:

$ lsblk -o MOUNTPOINT,PKNAME | grep "^/"[^[:alnum:]]
/                 dm-0

Use awk to print and assign the 2nd column, PKNAME, to a variable:

$ pkname=$(lsblk -o MOUNTPOINT,PKNAME | grep "^/"[^[:alnum:]] | awk '{ print $2 }')
$ echo $pkname
dm-0

2. Find the PKNAME for the previous PKNAME

Use lsblk again, this time with PATH, PKNAME, and KNAME as columns. Use grep to find lines containing the value of $pkname:

$ lsblk -o PATH,PKNAME,KNAME | grep $pkname
/dev/mapper/dm_crypt-0            sda3   dm-0
/dev/mapper/ubuntu--vg-ubuntu--lv dm-0   dm-1

This results in two matches, but we only want a match where $pkname matches the 3rd column, which is KNAME. The 2nd column, PKNAME, has to be included, because that's the next value needed.

Use awk again to get that value, and re-assign it to your variable:

$ pkname=$(lsblk -o PATH,PKNAME,KNAME | grep $pkname | awk -v val="$pkname" '$3 == val { print $2 }')
$ echo $pkname
sda3

3. Find the PATH for the previous PKNAME

Use lsblk to display PATH and KNAME columns, grep to find the matching line, and awk to print the first column, PATH:

$ lsblk -o PATH,KNAME | grep $pkname | awk '{ print $1 }'
/dev/sda3

Finally, combine all of the commands together, separated by semi-colons. To be complete, tack on an unset at the end to clear the variable, $pkname. There's your one-liner without needing root access.

$ pkname=$(lsblk -o MOUNTPOINT,PKNAME | grep "^/"[^[:alnum:]] | awk '{ print $2 }');pkname=$(lsblk -o PATH,PKNAME,KNAME | grep $pkname | awk -v val="$pkname" '$3 == val { print $2 }');lsblk -o PATH,KNAME | grep $pkname | awk '{ print $1 }';unset pkname
/dev/sda3