I have a living room on my first floor that is 11.5 x 16.75 and I am going to put a loft to cover the entire area. The room has 3 walls and a staircase on the fourth wall area. The joists will run the short way, the staircase is on the short wall at the end of the long wall. I need to know how to secure the new joists to the existing walls. I was thinking of putting up a ledger type board with lag bolts? Then attatching joists with joist hangers to the ledger board. Forgive me if I am not using the right verbage. Any thoughts?

Some people do it this way, but personally I don't like a whole floor being held up by lag bolts. What I would do is to nail the joist to the side of the existing stud, and then cut another stud and position it under the joist, then nail the second stud side by side to the first. It's a bit of an overkill but it does two things - gives support to second floor, and stiffens the existing wall for all the additional weight. Of course all this assumes that you have sized the new joist properly and verified that the existing wall and foundation can take the new weight.

As Jay said. Be sure that the wall your bolting the new floor rim joist to is a weight bearing wall. If this wall your bolting to is simply placed over the center of the basement with no supports below to the floor of the basement its most likely not a weight bearing wall. This will cause the wall and floor to sag once you bolt the new floor to it.
This ideally should be drawn up and evaluated by a licenced professional engineer before you make any expensive mistakes. Besides you need permits to do this and the township will require such drawings in order to approve this application.

They are all load bearing walls. Is it a bad thing to use the lag bolts, or just your favored way of doing things? If I were to put in more studs, I would have to tear down all the drywall on the first floor in the room, I do not want to do that. Any other thoughts?

You need to support the joist either by support columns or framing. Simply lag bolting the rim joist to the wall is not going to be enough support.You must tear down the wall that your fastening to. You have no idea what or how the wall was framed. Simply taking a chance on thinking the wall was done correctly is a big mistake for the cost of a few boards of rock.
As it has been said many time here, Get a design professional to draw up what is needed before you proceed. It may cost a few hundred dollars but when its done, you know you will not have any floor failures. Both your family and your insurance company will thank you for it.

You have to do more than verify the construction of the bearing wall, you have to find out if your foundation and footing can take the load of an extra floor. Since the vaulted ceiling already rests on these walls you can assume that it's at least designed to support that, but is it designed for an additional floor? Is it a 2x4 wall or 2x6?

But getting back to the lag bolt question, I personally think that it's a bad idea to use them in this case because you have a whole floor with furniture, people and pets resting on the shear strength of lag bolts. Secondly, how do you know how many to use? Too few and you risk collapse from the lag bolts failing, too many and you risk your ledger failing because of the weakened state you put the ledger in where it comes into contact with the stud. Also I would absolutely not leave the sheetrock on the wall and bolt the lag bolt to the studs with that behind it. The sheetrock has absolutely no structural properties whatsoever, leaving 1/2" of the lagbolt "exposed" before it enters the bearing stud - this is a big no no. Now you've entered a bending moment into the lag bolts that wasn't there before. Clear as mud?

But, assuming that you've verified that existing conditions will allow an extra floor, you don't need to tear off the sheetrock down to the floor, just a foot or so below the bottom of the new floor, a good taper can fix that joint such that you never know it was there. You'd have to sheetrock the new ceiling anyway.

One last thing, I do remodels all the time and this is the type of job that I bring a structural engineer in and have a site inspection done, then get a letter stating that site conditions will allow the new project. You just can't go in blindsighted and hope it will hold, peoples lives are at stake - pay the $200 to have a professional look at it.

Architects can design it too.