If cd ~ places you into /home/ls, then in that session, the $HOME environment variable has been set to /home/ls somehow. That might be caused by the home directory being set to /home/ls in the user account information in /etc/passwd (or whatever plug-in mechanism is used for user account information), or by something changing the environment variable to an incorrect value, either for that specific session only, or for all login sessions.
If you don't have write access to /home/ls and the /home/perdiem directory exists and is writeable to your regular user, then I would suspect an error in a customized login script or a mistyped command causing the $HOME environment variable to get reassigned.
If /home/perdiem does not exist and /home/ls does, and the latter has the correct ownership and permissions to serve as your home directory, then it would suggest an error in script(s) responsible for creating the user account. In this case, the /etc/passwd line for your user account would also specify the home directory as /home/ls.
You could check this with getent passwd perdiem and looking at the 6th colon-separated field on the output line.
An output like
perdiem:x:1000:1000:Full Name,,,:/home/perdiem:/bin/bash
would mean the home directory is specified correctly in user account information, and so something must have changed the $HOME variable after the login session was initiated.
A result like
perdiem:x:1000:1000:Firstname Lastname,,,:/home/ls:/bin/bash
would mean the error is in user account information, suggesting an error at user account creation time.
Debian/Ubuntu seems to supply /usr/sbin/adduser as a wrapper script for user creation and treats /usr/sbin/useradd as a low-level tool. Errors in customization of this script (either by you, or by the WSL distribution packager) might cause the script to call the low-level useradd command with wrong parameters.
But if this was the initial user account created during the installation of the WSL environment, then the user account may have been created directly by whatever script(s) are used in the installation process, which may or may not involve the useradd command or the adduser script at all.
lsas a username seems odd ...