Sorry, I just realized that I wasn’t being very clear when I wrote my question… LAMP has its own password (part of MySQL), and I cannot log into it. Typically when installing LAMP on your own a dialogue requesting a password comes (but when using the Digital Ocean auto-install tool, this does not occur).

Yes. The password you would set up when installing mysql-server on ubuntu is the root MySQL password. This is displayed in the MOTD on your droplet when you log in via ssh. An example is below:

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Thank you for using DigitalOcean's LAMP Application.
Your web root is located at /var/www/html and can be seen from http://104.131.61.241/
The details of your PHP installation can be seen at http://104.131.61.241/info.php
Your MySQL root user's password is vxQO7NRuEl
You are encouraged to run mysql_secure_installation to ready your server for production.
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To delete this message of the day: rm -rf /etc/motd.tail