The script /etc/lightdm/xsession has been removed; lightdm now tries to run 'lightdm-session', that should in theory be in the PATH, but it's not installed at all.

lightdm version 1.6.1-4

Log evidence:

--------------------------------------------------------
[+0.00s] DEBUG: Logging to /var/log/lightdm/lightdm.log
[+0.00s] DEBUG: Starting Light Display Manager 1.6.1, UID=0 PID=1759
[+0.00s] DEBUG: Loaded configuration from /etc/lightdm/lightdm.conf
[+0.00s] DEBUG: Using D-Bus name org.freedesktop.DisplayManager
[+0.00s] DEBUG: Registered seat module xlocal
[+0.00s] DEBUG: Registered seat module xremote
[+0.00s] DEBUG: Adding default seat
[+0.00s] DEBUG: Starting seat
[+0.00s] DEBUG: Starting new display for greeter
[+0.00s] DEBUG: Starting local X display
[+0.00s] DEBUG: Could not run plymouth --ping: Failed to execute child process "plymouth" (No such file or directory)
[+0.00s] DEBUG: Using VT 7
[+0.00s] DEBUG: Activating VT 7
[+0.01s] DEBUG: Logging to /var/log/lightdm/x-0.log
[+0.01s] DEBUG: Writing X server authority to /run/lightdm/root/:0
[+0.01s] DEBUG: Launching X Server
[+0.01s] DEBUG: Launching process 1763: /usr/sbin/X :0 -auth /run/lightdm/root/:0 -nolisten tcp vt7 -novtswitch
[+0.01s] DEBUG: Waiting for ready signal from X server :0
[+0.01s] DEBUG: Acquired bus name org.freedesktop.DisplayManager
[+0.01s] DEBUG: Registering seat with bus path /org/freedesktop/DisplayManager/Seat0
[+0.37s] DEBUG: Got signal 10 from process 1763
[+0.37s] DEBUG: Got signal from X server :0
[+0.37s] DEBUG: Connecting to XServer :0
[+0.37s] DEBUG: Starting greeter
[+0.37s] DEBUG: Started session 1772 with service 'lightdm-greeter', username 'lightdm'
[+0.38s] DEBUG: Session 1772 authentication complete with return value 0: Success
[+0.38s] DEBUG: Greeter authorized
[+0.38s] DEBUG: Logging to /var/log/lightdm/x-0-greeter.log
[+0.38s] DEBUG: Session 1772 running command /usr/sbin/lightdm-gtk-greeter
[+0.42s] DEBUG: Greeter connected version=1.6.1
[+0.42s] DEBUG: Greeter connected, display is ready
[+0.42s] DEBUG: New display ready, switching to it
[+0.42s] DEBUG: Activating VT 7
[+0.81s] DEBUG: Greeter start authentication for legolas558
[+0.81s] DEBUG: Started session 1791 with service 'lightdm', username 'legolas558'
[+0.82s] DEBUG: Session 1791 got 1 message(s) from PAM
[+0.82s] DEBUG: Prompt greeter with 1 message(s)
[+3.21s] DEBUG: Continue authentication
[+4.74s] DEBUG: Session 1791 authentication complete with return value 0: Success
[+4.74s] DEBUG: Authenticate result for user legolas558: Success
[+4.78s] DEBUG: User legolas558 authorized
[+4.85s] DEBUG: Greeter requests session xfce
[+4.85s] DEBUG: Using session xfce
[+4.85s] DEBUG: Stopping greeter
[+4.85s] DEBUG: Session 1772: Sending SIGTERM
[+4.86s] DEBUG: Greeter closed communication channel
[+4.86s] DEBUG: Session 1772 exited with return value 0
[+4.86s] DEBUG: Greeter quit
[+4.90s] DEBUG: Dropping privileges to uid 1000
[+4.90s] DEBUG: Calling setresgid
[+4.90s] DEBUG: Calling setresuid
[+4.90s] DEBUG: Restoring privileges
[+4.90s] DEBUG: Calling setresuid
[+4.90s] DEBUG: Calling setresgid
[+4.93s] DEBUG: Dropping privileges to uid 1000
[+4.93s] DEBUG: Calling setresgid
[+4.93s] DEBUG: Calling setresuid
[+4.93s] DEBUG: Writing /home/legolas558/.dmrc
[+4.93s] DEBUG: Restoring privileges
[+4.93s] DEBUG: Calling setresuid
[+4.93s] DEBUG: Calling setresgid
[+4.98s] DEBUG: Starting session xfce as user legolas558
[+4.98s] DEBUG: Session 1791 running command lightdm-session startxfce4
--------------------------------------------------------

Workaround:
I created executable script /etc/lightdm/xsession with content:
---------
#!/bin/sh
source $1
---------

and enabled it in lightdm.conf as session-wrapper

NOTE 1: an xsession script was in place and working, since I found it enabled in lightdm.conf, but at some point it must have been removed by the package (I never removed it manually)

NOTE 2: this is unrelated to bug #36659, as it happens with any session