OK, Now I understand what you are doing.
What you are doing is what you are supposed to do. However, in some cases, as you found, an Mac can not print to a network printer over wireless . This is documented on some Apple forums. (IP is not enough. Read on.)
To print the one document you could use a thumb drive to transfer it to another computer, PC. Likely you have already done that . Now you want a permanent solution the student can always use.
Frankly, I am not qualified to find the solution. Of course, the Mac will print directly to the Lexmark E342n using a USB cable. Is that right?
Here is a item that maybe relevant to your problem.
http://discussions.apple.com/message.jspa?messageID=8299639Topic : Lexmark Wireless X4550 printer wouldnt work with Airport Extreme Network
Here is a detail found in that link. It is not enough to have just the IP.
Example:
Device URL: lexnet3://192.168.5.110:1
You will have to read down through nit to find that detail.