Lexmark is junk, first of all. If it's still within the return period, i'd suggest returning it for a refund and purchasing another. I've been doing tech support for over 15 years, and every time I hear Lexmark, I cringe.
But, beside my personal hate for the brand.. Sounds like there's a sensor error in the print head. For whatever reason, it's not able to properly detect the cartridge. First check the manual it came with for troubleshooting tips. There may have been a step you forgot during setup, or something similar. If that does not yield results, you should give technical support a call and see if they know of an issue with the printer model, or have a work around for it.
All else fails, if it's recently purchased and you can return it to the store, tell them it's defective and you'd like a replacement for it.
As a side note, cnet review of this printer:
With so many other inexpensive photo inkjets on the market today, we can't recommend the Lexmark z2420--it's prone to paper jams, prints at a snail's pace, and produces unacceptable quality prints.