Where is your app deployed? If it is on your customer's premises, then the easiest might be to do an LDAP query against AD (an LDAP server) like @nzpcmad suggests. Tomcat has support for Windows Authentication too if I'm not mistaken, so it might be easier to go that path.
If it is off-premises, you will have to use an identity federation approach. You will have to change your app to accept SAML tokens and implement the SAML protocol (because you are in the Java world that might be the best option). Your customer will need to deploy an STS (like ADFS).
It really depends on how your app is designed and accessed by your customers (on-prem vs hosted, single tenant vs multi-tenant).