Yes, liveSite's built-in RSS feature will allow you to dynamically publish content to your Facebook page.
First, you will need to enable RSS for a Custom Form. Please search the built-in liveSite help documentation for "RSS" and read the article titled "Create/Edit Custom Form Field" for information about how to enable RSS on a Custom Form. After your Custom Form is RSS enabled, then you will need to make a few posts so that you can later verify that Facebook can find your Form List View Page.
Now, you will need to create a Form List View Page that contains the RSS enabled Custom Form Fields.
Once your Custom Form and Form List View Pages are created, then login to your Facebook account, and click on the "Account" tab in the top right hand corner of the screen. When the sub-menu appears click on the "Application Settings" option, and then after the page loads click on "Notes".
You should now be on the "Notes" homepage. Near the right sidebar you should see a box with the heading "Notes Settings". Inside of that box click on the "Import a Blog" link. Next you will be asked to enter the blog URL. Enter the URL of the Form List View Page that you created earlier, and then click on the "Start Importing' button. It may take a few moments for the next page to pull up as Facebook is reading the RSS you gave it.
Next Facebook will show you a preview of what the blog will look like once it is imported. Click "Confirm Import" to complete the import.
Now your Custom Form is connected to your Facebook notes. By default your "Notes" will appear on your "Wall". You can change this in the "Notes Settings" in the "Application Settings" tab.
Please be aware that it can take Facebook up to 24 hours to start pulling in your content. Also, new posts made to your Custom Form may take up to 8 hours to be published to your Facebook "Notes".