trying to add my thunderbird work email account to my new iphone, how do I find my "incoming mail server" and "outgoing mail server" host names?

First off there is no such thing as a Thunderbird email account. Email providers issue email accounts and Thunderbird is email client software and not a provider. You can look at the server settings in Thunderbird to see the settings it is using or you could get a list from your provider. In Thunderbird go to the menu bar and select Tools-Account Settings-Server Settings to see the Inbound settings and Tools-Server Settings-Outbging Server(SMTP) for Outbound settings. No menu bar with Tools showing? Press the alt key.