The right-click menu in the Laserfiche Client cannot be customized at this time. The best way to add this functionality is to add a button to the toolbar. Custom buttons that perform complex operations like the one you're describing can be added to the toolbar using the Client Automation Tools library found in the Laserfiche SDK. We don't have any specific examples of an integration like this, but the SDK documentation has examples of custom buttons and toolbars.

If you do not want to create your own custom integration, Workflow would be the other option. You can create a business process that emails a document upon clicking a button on the toolbar. Workflow has the capability to auto-populate fields and attach documents. This would achieve the kind of ease-of-use the right-click drop down provides.