I've always made it on the spot and cooked it then and there, but would like to make at home and take it to a large party the next day and cook it then - will it work?
Yes, and I find it taste better. When I make lasagna I will not fully cook the pasta. Instead, I keep a pot of boiling water and I dip the pasta into it to soften while I'm assembling the dish; the pasta is in the water for less than one minute. The pasta seems to absorb more of the sauce, keeping the flavor but making a dish that does not fall apart as easily.
Absolutely, it will work! You can keep it in the refrigerator, ready to bake, for a couple of days.
It also works very well to freeze it at that point, to defrost & bake at a later date.
The only catch is that the baking time may need to be extended a bit, since you'll be working with a product that is refrigerator-cold, as opposed to freshly cooked.
My wife and I have made lasagna for over 100 people on a few occasions. The way we have done this is to make several full pans of the product and then freeze them down for later use (up to two weeks). We have seen great success with his technique.
As far as making it one day and then cooking it the next (without freezing), this is actually a real good way to do it. However, I wouldn't wait more than 48 hours, as the breakdown will start to occur at this stage.
We did this when I worked prep in a restaurant. Half cooked the pasta and pre-cooked the meat layer. Assembled it cold and refrigerated over night. It took about 45 minutes to cook on 350 f. It was also covered in plastic wrap first then a layer of tin foil. This helped keep it moisture while storing and cooking. It does seem to taste much better.