LAM provides configuration export and import. Use this to transport the configuration to your new server.
To manually move LAM (Pro) from one server to another please follow these steps:
Install LAM (Pro) on your new server
Copy the following files from the old server to the new one (base directory for RPM/DEB is /usr/share/ldap-account-manager/):
config/*.conf
config/config.cfg
config/pdf/*
config/profiles/*
config/selfService/*.* (needed for LAM Pro only)
The files must be writable for the webserver user.
Open LAM (Pro) login page on new server and verify installation.
Uninstall LAM (Pro) on old server.