“All work and no play makes me want to chop some trees.”
–Lucy the Axe
Lucy the Axe is a character-specific item that Woodie begins the game with. Lucy has infinite durability and in Woodie's hands, cuts Trees extraordinarily fast. Lucy is a sentient being, and although it is not known if this is real or just Woodie's imagination, it is likely real as in DST, others can see her quotes. When equipped, Lucy will speak a line such as 'I missed you', 'Did you miss me?' and 'You came back!'.
Lucy will egg Woodie on when he chops down Trees, until he has almost reached the point at which he will become a Werebeaver. When the transformation is almost ready to occur, Lucy will begin to warn Woodie.
Lucy can be used as a melee weapon, dealing half the damage of the regular axes.
Lucy is based on a traditional fire axe, having a red blade with a silver edge, and a wooden handle. Lucy speaks with red text that appears below Woodie, to avoid confusion with Woodie's white text, and is given a shrill, instrumental sound effect whenever her lines are spoken.
When not in the player's inventory, Lucy will be indicated on the map by an icon. This can be useful to indicate where the player's items were dropped at the point of a Werebeaver transformation.
Lucy reappears in the Forge event as Riled Lucy, Woodie's primary weapon. Riled Lucy can be thrown or "chucked" at enemies for damage at a distance. This ability also sets the aggro of the creature hit to Woodie, making her useful for kiting. However unlike previous incarnations of Lucy, she can be picked up and used by other characters. Also unlike previous incarnations of Lucy, she does not speak.
Whether Lucy is speaking in real life or not is, as of yet, unknown. There has been plenty of speculation on the matter, ranging from insanity, through curses, to past relationships. The devs have been cagey on the subject, but they have said that Woodie is fairly levelheaded, Lucy's talkativeness aside.
Lucy's DST quotes for other characters imply that Lucy can actually talk.
Lucy is the first item that can speak and has distinct lines, not just sound effects, like the Living Log's scream.
Lucy does not appear to recognise Woodie when he is a ghost.
Lucy is voiced by a musical saw.
When playing Adventure Mode, Lucy will not use a slot in the Teleportato. She will appear in Woodie's inventory after arriving in the new world.
Lucy's line, "All work and no play makes me want to chop trees", is a reference to the English proverb "All work and no play makes Jack a dull boy". This may also be a reference to the pivotal scene in the Stephen King film The Shining, where insane character Jack Torrance types this line many times, and later uses an axe similar to Lucy as a weapon.
Kevin Forbes added Lucy for Woodie's special item because he "liked the idea of a half-crazed lumberjack being egged on by his axe."
Based on his examination quote, Maxwell seems to have known Lucy beforehand.
One of her quotes for Woodie changing back from the Werebeaver ("I think that creepy girl is mad at you.") is a complement to Wendy's quote for the Werebeaver ("He pinky-promised I'd get to ride on his shoulders next time. Such lies.").
Unlike in regular DST, other players can actually wield and throw Riled Lucy in the Forge. However, she will not return to their hand if she is thrown, and will need to be manually picked up.
Riled Lucy in the Forge does not talk. However, her speech files reveal that she has lines for various situations that were cut because the developers felt that they created too much clutter. 
↑Kevin on the forums: "I'm glad you guys are liking him so far. If I recall correctly, Corey suggested we make him a werebeaver one night when we were talking about making new characters craaaazy so that they would market well. I think he may have been joking, but I loved the idea so much I got the artists to draw it.I added Lucy after I started adding special items for the other characters. I just liked the idea of a half-crazed lumberjack being egged on by his axe. We asked our music guys for the hoedown music on Friday, as a last minute effort to put the craziness over the top. I didn't think we'd get it back in time for the update, but our music guys are really really good (and fast!). I was intended to be a hillbilly / DS take on the classic Super Mario brother's invincibility star theme.Now all I have to do is fix the bugs and write the dialog :)" Posted on June 26, 2013.
↑Riled Lucy, the one that doesn't talk thread on Klei Forums. Dev Scott Hansen on the unimplemented quotes: "At one point we had more character banter but all the text just got in the way and felt like spam." Posted on November 26, 2011.