from what i can see everything looks to be configured correctly.
There are a few questions from my initial reply you have not answered though:
Who is your host? in a lot of cases, you can leave the SMTP Server setting blank, but some hosts will require that you enter it. 
I can see from your code, that the smtp server address are left blank, like i said, in some cases this is fine, in others you need to enter an smtp server address, you would need to check with host to see if an SMTP server address is required or not when sending an email using a php script, and if it is required, they will be able to tell you what address to use.
What have you entered for the from address? many hosts will require that the from address be a valid email address for your domain.
in the code, i see the from address you are using is poppoll@lilies.org, is this a valid address for your domain?
On the SMTP Server settings tab, there is an option to "Include the From address as an extra parameter" depending on your host, you may need to check this.
i see that this option has not been checked, you may need to, again, you need to double check with the host to determine if this option is needed or not.
