John's sales literature says,  " .......Under sail the Northeaster Dory is fast, stiff, and close-winded........" 

"Stiff".......usually means it resists heeling well. The opposite of tippy.

"Close winded"...... would mean it can point well to the wind.  Errrrr.........sails higher up wind.   For example 45 degrees off the wind instead of 65 degrees.  ("higher" has nothing to do with freeboard or heeling.)

What happens when you let go of everything depends upon conditions point of sail,  sail set/trim, and board depth.  I suspect the boat has "weather helm" and will round up under most conditions.  A lee helm would fall off.

What will happen on the ne dory if i were to let go of both the tiller and sheet on the lugsail. I would like to try this when the water warms up a bit more in the far north.

It is a bit hard to say because every boat design will react a bit differently.  The same boat may even react differently depending on wind strength and how it is loaded.  You do not need to wait for warm water to try this because nothing bad will happen quickly unless the winds are really blowing. 

Is there also an easy non technical explanation for lee and weather helm.

Lee helm means the the boat will start turning away from the wind if you let go of the tiller.  Weather helm means that the boat will turn into the wind if you let go of the tiller.  The terms, come from the direction that you have to push a conventional tiller to keep the boat sailing straight.  With weather helm, you must push the tiller towards the windward (weather) side of the boat to keep it sailing straight.  With lee helm, you must push the tiller toward the leeward (lee) side of the boat.  Generally speaking, a little weather helm is considered good since the boat will slowly turn towards the wind and the sails will spill the wind if you let go of the tiller.  Lee helm is bad because the boat will turn downwind which will put more wind into the sails.     

Lastly what is meant by the ne dory being stiff winded.

"Stiff winded" is not really a standard term.  A boat is call "stiff" if it stands up well to wind (doesn't heel much).  A boat is called "close winded" if it can point well (it can sail with its bow pointing close to the wind).

It sounds like you are getting into sailing.  If that is the case, I stroingly recommend that you get some lessons.  You may also want to buy a good introduction to sailing type book.  A few years ago I bought "Sailing for Dummies" for my new wife.  It is actually quite good if you can get past the title.      

Mark and Grumpy have answered your questions, but I'll add a couple of additional points. If you are new to sailing, the lug-rigged Northeaster Dory is a great boat for you. The lug rig is simplest and most forgiving sailboat rig you can find. If the wind is blowing, put the sail up. If the wind is too light, you can drop the sail and row. If you start getting alarmed by a strong gust, you let go of the mainsheet and the boat immediately settles down. It's usually best to keep hold of the tiller, but you can often let it go for a couple of seconds with no worries.

I just returned from a two-day cruise-camping trip in my dory. On the first day I was beating into a gusty north wind -- probably 15 mph average wind speed with gusts up to 30. The very fact that I could sail 12 miles upwind in those conditions is testament to the  genial handling of this small sailboat. (But it was a bit of work sailing!)

One thing you can do to  see what happens when you let go of the sheets is to position the boat while on the trailer so the winds is at a close hauled or close reach position [see diagram] then put your sail up.  Hold on to the  sheet then let it go.  Obviously the boat is not going to move but it will give you and idea of what happens to the sail when you let it luff.  All the pressure is let go.  Then study the points of sail and when you get a chance on the water do the same experiement, so you understand what happens at all the major points of sail.  Good luck!

>>>>Lee helm means the the boat will start turning away from the wind if you let go of the tiller.  Weather helm means that the boat will turn into the wind if you let go of the tiller. >>>>

This is correct, but some clarification is helpful:  The above is true if the sails are trimmed properly and the boat is in motion.   

There's a good bit of confusion over "lee helm" and "weather helm." I've had builders report lee helm on one boat or the other, and only after a long dialogue did I realize that they were describing the boat's behavior when it was stalled or stopped, sails luffing.  

If you have a boat with a mast mounted forward of the middle of the boat, and you ease the sheet until the sail luffs, and the boat slows until the daggerboard/centerboard/keel is no longer generating lift, the bow of the boat will fall off of the wind.  This is not "lee helm."  This is a boat that is stalled, and like an airplane that's lost lift over its wings, the nose is going to drop and start heading downwind.

Catboats (any boat with a single sail) also have a failure mode that can be mistaken for "weather helm": you've come to a stop with the sail luffing. You sheet in to get moving again;  the leech of the sail fills first.  This pulls the stern to leeward and the bow into the wind.  Again, not "weather helm"; the boat is just stalled. One specific iteration of this stalling condition is called "being in irons." Catboaters learn to bear off while sheeting in to build some speed over the foils and avoid getting stuck in irons.

Now, assuming you're trimmed properly (not pinched, not luffing), and the boat has enough speed for the centerboard to work, a tendency to turn into the wind is weather helm.  A little bit is actually ideal.

Likewise, if you're trimmed on your course and making knots and the bow wants to turn away from the wind, that's lee helm.

   Everyone learns differently, but I'd suggest starting with one of the several classic intro books to sailing.  I'm a reader and visual sort, engineer by education and trade, so it's the first place I go.  There are scads of how-tos on the Web, but I'd go for a real, classic book.  The best sailing authors gave these books a lot of thought and work, and it beats dropping your tablet in the drink trying to watch the YouTube and do it!  :-) 

I actually got started as a kid on a Sailfish, so learned by doing, but as adults, I think we benefit from some coherent explanation up front.  I like Steve Colgate's classic Fundamentals of Sailing, Cruising, and Racing. Also Bob Bond's Handbook of Sailing. Both will take you much farther than just a dory, but I'm a sucker for good books.

If you either already have some intro to the physics of fluid flow, or read the intro explanations in these books, you can start visualizing what's going on with your sail, rudder, and centerboard as you experience it, and it will help you understand the dynamics John is explaining in his good message above about lee and weather helm.  

If you are a YouTube sort, the Royal Yachting Association (RYA) has a fistful of dinghy videos that are good, though many are in the context of racing dinghies.  Search for RYA dinghy sailing on YouTube.  This link should go to the first one:

https://youtu.be/EfJIu_moZaE