Joe, with lath and plaster walls and installing T&G siding. You have to have something to nail into. If you visualize your lath and plaster walls without the lath and plaster, you will see that you have vertical studs every 16" on center nailed to a head plate and toe plate on the top and bottom. Putting a nail into the lath and plaster alone is not sufficient. You have to nail into wood.
T&G siding was made to be installed vertically but you can only nail into the top and the bottom, plus whatever studs you happen to be able to hit. So, you can tear down all your lath and plaster, install horizontal blocking in your walls and install the siding correctly.
The other option is to install the siding horizontally. You do have something to nail to. But wood expands and contracts. While it does move the most, percentagewise, across it's width, it moves along it's length also. A T&G is made to allow for the movement in width but you have to be aware of where you are and how the wood is going to move when you install it. However, since you don't normally have a T&G joint at the top and bottom of the board, you either have to make one or know that you will have gaps at the butt ends of the boards in some seasons.
OK, now to nails. You do want to nail at an angle through the tongue to hide the nail head, you want to have about 3/4" of nail or more in the stud. How thick is the lath and plaster? How thick is the lath and plaster with the drywall over it? If you buy a finish nail that is long enough to get through all that, will it be so big a diameter that you will tend to split or crack your very expensive T&G siding? The answer to the last question is yes.
There are a lot of questions and negatives in this and one easy, simple answer. Instead if T&G siding, just install paneling. Paneling comes in 3/4" thickness and most is milled so that there is a groove every 16" to hide the nail heads. The better paneling is not cheap but the T&G is more expensive and you have to finish it. The paneling comes prefinished in just about any kind of wood you can think of. Cutting paneling to fit around doors, windows, electrical outlets and the like takes some work but you have the same or worse with T&G. Just something to think about.