You need to have SMTP server installed on the dev box so that it can receive email from the Lotus Notes box. Also, Lotus Notes box needs to know where to send the mail. So if you have firstname.lastname@example.org as the recipient URL, that mydevbox.com needs to resolve to your dev box.
I haven't tried this myself, but you might be able to just use HOSTS file on the Lotus Notes box, if it is a Windows server. Otherwise you will need a DNS MX-record defined so that Lotus box can resolve the domain mydevbox.com to your dev server's IP.
If there are issues, double check the SMTP settings so that it accepts the incoming mail from the Lotus box.
Then when your SMTP server receives the mail, it will place it in the "drop" folder in the server. SharePoint job will then check that folder and actually create a SharePoint list item based on that mail message by looking at the recipient e-mail in the message and the list of mail-to-sharepoint-list mappings you've configured.
This question will give you relevant info regarding setting up the local SMTP.