I use veggie (dried soya) mince. about 100g and then add a pint and a half of 'stock'. This is made up from:
Tablespoon of tomato ketchup. Ditto brown sauce. Heaped teaspoon of veggie bouillon. two-three teaspoons of Worcester sauce. Dessert spoon of DARK soy for colour. A dessert spoon of fish sauce. Boiling water. Pour over mince and stir until all liquid absorbed. I usually leave this a couple of hours.
I saute in oil, a finely chopped onion, two sticks of celery and a large carrot finely chopped. Add mince. Add a little liquid and simmer for 30 minutes. Add water if required, you want it fairly wet for lasagna as the pasta suck all the moisture out.
Make lasagna with that - although I make a proper bechamel, pint and half of milk, one large onion, carrot, stick of celery, bay leaf, sprinkle of nutmeg and a few peppercorns. This soaks the whole time the mince is soaking. I then bring it to the boil, let it stand for 20 minutes, sieve the whole lot, heat it back up, add 3oz butter, let it melt, whisk it smooth and then add the 2-3oz flour whisking as it goes in.
Make lasagna. Grate cheese on top.
Never any left over. Not ever...