Lotus Domino uses cookie-based authentication. When you authenticate with a Domino web server, an Ltpa Token is stored in your web browser as a cookie. Apache Tomcat uses its own form of authentication and can not reuse the Domino Ltpa Token for authentication. (LTPA is light-weight third party authentication) It's possible to "integrate" the web servers. The user will authenticate only once, and may then access the Domino and Apache Tomcat web servers.
The graphic above shows 2 Domino servers, and 3 Tomcat servers. They each have their own host name. The user may start at any web server, login once, and then access any of the other web servers. They are not prompted to login again.
Apache Tomcat 5.5.25, and Domino 6.5.3 or 7.x
Apache Tomcat 5.5.26 or later, and Domino 8.x
Apache Tomcat 6.0.18 or later, and Domino 8.x