My biggest critic's (wife) only complaint with my lasagna is that she doesn't like that it stands in a tower in the pan.
This is because I use three noodles wide, and when they are put next to each other, they don't meet the edges of the pan. (13x9 glass pan)
What technique should I use so that the lasagna fills the pan?
For par-cooked noodles, you just cut them to size. You may need to trim a corner to fit, cut them to length, or even split them the long way to get them to fit.
No-boil noodles are the more difficult situation:
The easiest way is to break them, but if you're picky, you may want to use the counter edge or a cleaver to try to get a more precise break. (but this doesn't always break where you expect it to)
The few times that I've done no-boil lasagna, I've opted to break pieces across the narrow direction of the sheets rather than trying to split the long direction. If you then use these pieces down the middle of the pan, leaving full sheets on the edges, it's much more difficult for people to see what you've done. (and easier to break)
As I change the orientation between the noodle layers, you often need to shorten some of the sheets anyway, so this becomes the filler bits. And if necessary, you can overlap the broken bits some, as you have the flat middle pieces to work with, not just the frilly edge that so many commercial lasagna sheets have.
You may want to save the 'better' broken pieces for the last layer, if you care about the final appearance (and won't be smothering it in so much sauce and cheese that no one will notice)
The layers also don't need to be completely gap-less; the pasta will expand when it cooks, so leaving a little bit of a gap (when using no-boil pasta) is typically a good idea.
You have a couple of options here, depending on what lasagna recipe you use. Some are more firm than others, and whether it fills the pan can influence the quality of your final dish.
From the sounds of it you have a lasagna recipe that is quite firm, and is able to stand on its own without touching the edges of the pan. This does mean that during baking, the edges of the tower will crisp up more, and any way you "solve" this issue will lead to an end product that will taste and feel different.
Sauce it up
What I often see in restaurants re-heating batch prepared lasagna in oddly-shaped containers is that they fill the void with sauce. Ragout, tomato, or white sauce are all options you can use here depending on the style of your lasagna. Downside is that it gets a lot sloppier and you might end up with something that is more akin to pasta bake than lasagna. Also the ratio of sauce-to-noodles might be off and not to everyone's taste.
Smaller pan
The obvious solution, get a smaller pan that fits your lasagna. Not the cheapest option, and probably not suitable for people with limited cupboard space. Will work splendidly with the first option if there is less edge space and the pan is only slightly too big. Alternative is to fill the void in your pan with something like tinfoil, but this is a botch job and there are some warnings out nowadays against using tinfoil in cooking.
Cut your pasta
You can always opt to cut the pasta sheets to fill the entire layer. Especially for firmer lasagnas, which by the sounds of it you have, this works splendidly. For looser lasagnas this might mean they have an increased likelihood of falling apart when baking or serving. This will mean you get a wider lasagna and might need more of all ingredients to achieve the same height.
Make your own pasta
As suggested by Joe in the comments, you can always make your own pasta. It's not incredibly difficult if you have a pasta roller, and you can make it any shape that fits your pan. I find that when using uncooked pasta, fresh, home-made pasta gets the best result.
Deal with it
From the sounds of it, your wife's only complaint might be just that it looks weird. If the end result is a splendidly tasting lasagna, but it looks odd, it's really not an issue. Do you really want to miss out on those nice crispy edges? I'd say experiment with some things, but if nothing actually improves the flavour, just deal with it looking weird and enjoy it as it is.
