Preheat oven to 375F/190C
Dice the squash and eggplant into fairly small cubes - around ½in/ 1cm. Dice the onion.
Roast squash in one dish and eggplant/aubergine and onion in another, drizzling both with a little olive oil, salt and pepper, for around 30mins.
When the vegetables are almost done, make the sauces. Warm the chopped tomatoes in a pan over a medium heat along with the basil, oil and sugar. Cook for a minute or two then set aside.
In another pan, melt the butter and once starting to bubble, add the flour. Cook for a couple minutes until starting to go nutty.
Reduce the heat and add the milk a little at a time. Once all added and smooth, add the Jarlesberg and stir in so that it melts. Set aside.
Once cooked, add the eggplant/aubergine to the tomato sauce and the squash to the cheese sauce.
Start layering up the lasagna - place half the eggplant/aubergine mixture in first, add a layer of pasta, then the squash mixture followed by another layer of pasta and finally the rest of the eggplant/aubergine.
Break up the mozzarella and dot over the top and then sprinkle over the parmesan.
When ready, bake in the oven for approx 40 mins until gently golden on the top.