I'm making a few assumptions here because your question doesn't really specify. Those are:
If those are both correct, your only option really is to connect to the LDAP server over SSL. This will obviously require setting up the LDAP server to be accessible over SSL if it's not already. The downside is that you ultimately have to embed the LDAP authentication credentials somewhere in your app.
On the other hand, if the DMZ server is a member of the company's Active Directory and the LDAP server you're connecting to is that same Active Directory domain, you should be running the Application Pool as a domain service account (with whatever AD permissions it needs for its task). Then, connecting to LDAP can be done via Kerberos and you wouldn't have to embed any credentials within the site to connect with.