LDAP has no relation to the ability to send an email, it only allows email address lookups and possibly authentication to the copier.
As for the email issue, it depends on the error you receive.
No communication is typically the DNS server: Properties > Connectivity > Setup > Wired Connection > Edit > IP (Internet Protocol) > Edit
Make sure you give the machine a domain name too, if you don't have one, just type WORKGROUP
Also, very important that the time and date is correct to within 3 minutes, if it is not, change it, the big pain with this is that the machine will need a reboot to set it. I can't fathom why time needs a reboot yet nothing else does to apply.
Properties > General Setup > Date and Time
At this point you can verify communication to the outside world via Smart eSolutions so go to Properties > General Setup > Smart eSolutions Setup and click on Test Communication Now
So now that we have the comm errors eliminated, the next thing will be authentication. I have no idea what your server requires, but Gmail is smtp.gmail.com on port 587 using TLS, and now SHA-2 encryption, the first 3 work on most of all the firmwares, but SHA-2 is a recent addition. So if your current firmware ends in 09100 you most likely will need an update.
But first, confirm the settings match exactly the following screens:
Login name absolutely has to match the previous screens email address
And lastly, the first time you setup an account it puts the from address in the email defaults, but if you make changes in the SMTP screens that does not update, so check in Properties > Services > Email > Setup and edit the From Field
And notice it probably does not match the other screens, change it and make it match
Then go send a test email from the machine and from CWIS (Last tab in screenshots 4-6)
If it works at the machine but not in the web interface or vice versa, the login names don't match on screenshot 5.
If everything is right, but it still fails you may as well just update the firmware, which can be done with the following linked tool that will do it for you, just run it from your PC and follow the directions. Once completed email will work for sure to gmail.
http://www.support.xerox.com/support/workcentre-7800-series/file-download/enus.html?contentId=132026