The Lexmark 6570 does not appear on the list of AirPrint compatible printers. See this Apple Support document for details:
You might still be able to print from the iPad to the Lexmark printer if you download and install an App like Print Central.
Another option might be Printopia. There is a free trial, so you will know in advance whether this will work or not. You need to have another Mac running on your network to be able to use Printopia.