I had some problems to setup Adminer in Docker. The instructions here should help setting it up faster.

Create a new directory called Adminer and put the following files into it:

Dockerfile:

FROM adminer
USER root
COPY login-password-less.php /var/www/html/plugins-enabled/login-password-less.php

login-password-less.php (The word admin in password_hash specifies the password, please change it for security reasons)

<?php
require_once('plugins/login-password-less.php');

/** Set allowed password
 * @param string result of password_hash
 */
return new AdminerLoginPasswordLess(
    $password_hash = password_hash("admin", PASSWORD_DEFAULT)
);

Then change dir in this directory and run:

docker  build -t my-adminer .

Assure that your SQLite3 database file is stored at /root/Data/Data.db and run:

docker run -ti --privileged -v /root/Data/Data.db:/Data.db  -p 8080:8080 my-adminer

Next open a browser and point it to http://localhost:8080. Set database driver to SQLite3, set field user to admin and password to admin or to the value you have choosen, set the Database field to "/Data.db" and press "Login".

Please mind that I had to use the docker --privileged option to get this working. So there have to be further measures for a secure setup.