How do I install Firefox 52 ESR on 16.04?

There is an official Firefox ESR PPA for supported Ubuntu versions: https://launchpad.net/~mozillateam/+archive/ubuntu/ppa

sudo add-apt-repository ppa:mozillateam/ppa
sudo apt-get update
sudo apt-get install firefox-esr

This firefox-esr PPA works for me on Xenial: https://launchpad.net/~jonathonf/+archive/ubuntu/firefox-esr

sudo add-apt-repository ppa:jonathonf/firefox-esr-52
sudo apt-get update
sudo apt-get install firefox-esr

but please note that you will not get security updates as this version is obsolete.

I have added this into my ansible playbooks, thanks for @galatians .

# Firefox ESR.
- name: add apt key of firefox-esr
  become: true
  apt_key:
    keyserver: "hkp://p80.pool.sks-keyservers.net:80"
    id: 4AB0F789CBA31744CC7DA76A8CF63AD3F06FC659

- name: add apt repository of firefox-esr
  become: true
  apt_repository:
    repo: "deb http://ppa.launchpad.net/jonathonf/firefox-esr/ubuntu {{ ansible_distribution_release }} main"
    state: present

- name: install third-party apt packages of desktop
  become: true
  apt:
    name: firefox-esr
    state: present

https://github.com/chusiang/hacking-ubuntu.ansible/blob/develop/tasks/setup_desktop.yml#L27