Create your custom error pages in Django, and use your context.

urls.py

from django.conf.urls import handler404, handler500

handler500 = website_views.server_error
handler404 = website_views.page_not_found

views.py

from django.http import HttpResponseServerError, HttpResponseNotFound
from django.template import loader

def page_not_found(request, template_name='website/404.html'):
    t = loader.get_template(template_name)
    context = {
        'your_var' : True,
        'request' : request,
    }
    return HttpResponseNotFound(t.render(context))

def server_error(request, template_name='website/500.html'):
    t = loader.get_template(template_name)
    context = {
        'your_var' : True,
        'request' : request,
    }
    return HttpResponseServerError(t.render(context))

How to use

1. Set DEBUG = False into settings.py
2. Run server using python manage.py runserver --insecure

Use the --insecure option to force serving of static files with the staticfiles app even if the DEBUG setting is False.
https://docs.djangoproject.com/en/1.10/ref/contrib/staticfiles/#runserver