I had no real intention to start a logomachy but now that it's good and going and seemingly friendly..
First of all the difference bewteen the noun and the verb is that the verb refers to the act, and most people would agree that the act has to be an intentional deceit.
The noun refers to the statement, and more people are willing to define a false statement as a lie. Regardless of whether it is intentional.
The problem is that one is inextricable from the other, if lie the noun can mean an apocryphal statement then the verb can mean the act of deliuvering one even without intent to deceive.
Now deb, your reading of your dictionary might be a bit convenient for you. I'd read the definition you quoted as supporting the notion that a simple falsehood consitutes a lie. I base it on the part of your definition that defines a lie as ";a falsehood". Before that it talks about intentional deceit but I take that part as a separate definition. Maybe I'm guilty of a convenient reading.
In any case I love that people here are willing to call a dictionary wrong. I never consider a Dictionary the final word, they disagree too often to be good gatekeepers.
If I were to define the word I'd make intent a prerequisite, but in usage I think many times it is applied simply when something is false.
Anywho, check out what Merriam-Webster's Collegiate® Dictionary thinks of this argument here:
http://www.m-w.com/cgi-bin/dictionary