Installing lsb-core on Ubuntu 14.04

What is the output of:

sudo apt-get update
sudo apt-get install lsb-core

Thanks

This is the output I get straight from the command line:

Reading package lists... Done
Building dependency tree
Reading state information... Done
Package lsb-core is not available, but is referred to by another package.
This may mean that the package is missing, has been obsoleted, or
is only available from another source

E: Package 'lsb-core' has no installation candidate

What is the output of:

cat -n /etc/apt/sources.list

Thanks

$ cat -n /etc/apt/sources.list
     1 #deb cdrom:[Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1)]/ xenial main restricted
     2
     3 # See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to
     4 # newer versions of the distribution.
     5 deb http://us.archive.ubuntu.com/ubuntu/ xenial main restricted
     6 # deb-src http://us.archive.ubuntu.com/ubuntu/ xenial main restricted
     7
     8 ## Major bug fix updates produced after the final release of the
     9 ## distribution.
    10 deb http://us.archive.ubuntu.com/ubuntu/ xenial-updates main restricted
    11 # deb-src http://us.archive.ubuntu.com/ubuntu/ xenial-updates main restricted
    12
    13 ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
    14 ## team, and may not be under a free licence. Please satisfy yourself as to
    15 ## your rights to use the software. Also, please note that software in
    16 ## universe WILL NOT receive any review or updates from the Ubuntu security
    17 ## team.
    18 deb http://us.archive.ubuntu.com/ubuntu/ xenial universe
    19 # deb-src http://us.archive.ubuntu.com/ubuntu/ xenial universe
    20 deb http://us.archive.ubuntu.com/ubuntu/ xenial-updates universe
    21 # deb-src http://us.archive.ubuntu.com/ubuntu/ xenial-updates universe
    22
    23 ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
    24 ## team, and may not be under a free licence. Please satisfy yourself as to
    25 ## your rights to use the software. Also, please note that software in
    26 ## multiverse WILL NOT receive any review or updates from the Ubuntu
    27 ## security team.
    28 deb http://us.archive.ubuntu.com/ubuntu/ xenial multiverse
    29 # deb-src http://us.archive.ubuntu.com/ubuntu/ xenial multiverse
    30 deb http://us.archive.ubuntu.com/ubuntu/ xenial-updates multiverse
    31 # deb-src http://us.archive.ubuntu.com/ubuntu/ xenial-updates multiverse
    32
    33 ## N.B. software from this repository may not have been tested as
    34 ## extensively as that contained in the main release, although it includes
    35 ## newer versions of some applications which may provide useful features.
    36 ## Also, please note that software in backports WILL NOT receive any review
    37 ## or updates from the Ubuntu security team.
    38 deb http://us.archive.ubuntu.com/ubuntu/ xenial-backports main restricted universe multiverse
    39 # deb-src http://us.archive.ubuntu.com/ubuntu/ xenial-backports main restricted universe multiverse
    40
    41 ## Uncomment the following two lines to add software from Canonical's
    42 ## 'partner' repository.
    43 ## This software is not part of Ubuntu, but is offered by Canonical and the
    44 ## respective vendors as a service to Ubuntu users.
    45 # deb http://archive.canonical.com/ubuntu xenial partner
    46 # deb-src http://archive.canonical.com/ubuntu xenial partner
    47
    48 deb http://security.ubuntu.com/ubuntu xenial-security main restricted
    49 # deb-src http://security.ubuntu.com/ubuntu xenial-security main restricted
    50 deb http://security.ubuntu.com/ubuntu xenial-security universe
    51 # deb-src http://security.ubuntu.com/ubuntu xenial-security universe
    52 deb http://security.ubuntu.com/ubuntu xenial-security multiverse
    53 # deb-src http://security.ubuntu.com/ubuntu xenial-security multiverse

Go for this page:

http://packages.ubuntu.com/trusty/amd64/lsb-core/download

and make the download ( x_64 Pc's ), if your pc is x_86 then follow this link :

http://packages.ubuntu.com/trusty/i386/lsb-core/download

the packet is .deb, easy for install, use the gedebi for it :)

You seem not to be running Ubuntu 14.04, but Ubuntu 16.04, and the problem you are facing is a known issue, Bug #1536353 and others.
Actionparsnip's workaround should help.