Can I connect to a Lexmark x4580 printer

Look in the app store. I recall there being a lexmark app.

https://itunes.apple.com/us/app/lexmark-mobile-printing/id469415392?mt=8

doesn't have the best of reviews. But there is also the option of a third party app like Print Central or Print n Share to allow printing to wifi printers

Lexmark may also have other options on their site.

You can install our LexPrint app to print using an iOS device and you'll also need to install our LexPrint Listener software to a host computer which will serve as a bridge for your printer and iOS device. Just go to http://bit.ly/Rm42lb for more info.