server.xml has two pertinent lines:
<Connector port="8088" protocol="HTTP/1.1" connectionTimeout="20000" URIEncoding="UTF-8" redirectPort="8443" address="0.0.0.0"/>
and
<Host name="localhost" appBase="webapps" unpackWARs="true" autoDeploy="true" xmlValidation="false" xmlNamespaceAware="false">
A key piece of information might be that this was all working before I decided Ubuntu 14.04 was not to my liking and I re-installed Lubuntu over the top (forgetting to backup my server.xml). Thus the router and DNS have both already been setup and were working prior to this attempt. It would seem that this step is not very popular for a variety of reasons. As a result, I am having a non-trivial amount of trouble locating this last step. Any help any of you can provide is much appreciated.
The A record was changed within a 1 day period (86400 seconds). Thus, from my PC and other computers I use, the TTL had not yet elapsed. This means I was cached in the recursive resolver. The cached A record was still pointing to a bad IP address. After being patient the site resolved when the cache was purged.
Next time I make a change to a record I will:
Lesson learned.