I removed lite-software and the package system repair was able to successfully complete. It did not fix the update errors, and installing lite-software returned the upgrade error.
I was refraining prom posting the full output as you don't have spoiler tags bbcode. Here is the full output:
~$ sudo apt-get update && sudo apt-get dist-upgrade
Hit:1 
http://us.archive.ubuntu.com/ubuntu xenial InRelease
Get:2 
http://us.archive.ubuntu.com/ubuntu xenial-updates InRelease [95.7 kB]   
Hit:3 
http://download.virtualbox.org/virtualbox/debian xenial InRelease        
Ign:4 
http://dl.google.com/linux/chrome/deb stable InRelease                   
Hit:5 
http://repo.linuxliteos.com/linuxlite citrine InRelease                  
Hit:6 
http://dl.google.com/linux/chrome/deb stable Release                     
Get:7 
http://us.archive.ubuntu.com/ubuntu xenial-backports InRelease [92.2 kB] 
Hit:8 
http://archive.canonical.com/ubuntu xenial InRelease                     
Hit:9 
http://ppa.launchpad.net/ubuntu-wine/ppa/ubuntu xenial InRelease         
Get:10 
http://security.ubuntu.com/ubuntu xenial-security InRelease [94.5 kB]   
Hit:11 
http://ppa.launchpad.net/danielrichter20...zer/ubuntu xenial InRelease
Hit:12 
http://archive.canonical.com xenial InRelease                           
Hit:13 
http://ppa.launchpad.net/iconnor/zoneminder/ubuntu xenial InRelease     
Hit:15 
http://ppa.launchpad.net/mati75/spacefm/ubuntu xenial InRelease         
Hit:14 
http://screenshots.getdeb.net xenial-getdeb InRelease                   
Hit:16 
http://ppa.launchpad.net/nemh/systemback/ubuntu xenial InRelease
Hit:17 
http://ppa.launchpad.net/otto-kesselgulasch/gimp/ubuntu xenial InRelease
Hit:18 
http://ppa.launchpad.net/webupd8team/java/ubuntu xenial InRelease
Fetched 282 kB in 6s (46.6 kB/s)                                               
Reading package lists... Done
W: Invalid 'Date' entry in Release file /var/lib/apt/lists/partial/us.archive.ubuntu.com_ubuntu_dists_xenial-updates_InRelease
W: Invalid 'Date' entry in Release file /var/lib/apt/lists/ppa.launchpad.net_ubuntu-wine_ppa_ubuntu_dists_xenial_InRelease
W: Invalid 'Date' entry in Release file /var/lib/apt/lists/partial/us.archive.ubuntu.com_ubuntu_dists_xenial-backports_InRelease
W: Invalid 'Date' entry in Release file /var/lib/apt/lists/partial/security.ubuntu.com_ubuntu_dists_xenial-security_InRelease
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Calculating upgrade... Done
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
1 not fully installed or removed.
After this operation, 0 B of additional disk space will be used.
Do you want to continue? [Y/n] 
Setting up lite-software (2.0-0200-linuxlite) ...
sed: can't read /etc/X11/Xsession.d/98vboxadd-xclient: No such file or directory
dpkg: error processing package lite-software (--configure):
 subprocess installed post-installation script returned error exit status 2
Errors were encountered while processing:
 lite-software
E: Sub-process /usr/bin/dpkg returned an error code (1)