Heat the butter in a pan. Add the flour to the butter and cook over a medium heat, stirring with a whisk; the flour must not take on any colour. Remove the pan from the heat. Pour in the milk all at once, bring to the boil while stirring, reduce the heat. Season the sauce, simmer over a medium heat for approx. 10 mins., stirring occasionally until the sauce is thick and creamy.
Cut half of the beetroot into slices 3 mm thick. Purée the remaining beetroot with 200 ml of the bechamel sauce.
Spread a little bechamel sauce in the bottom of the prepared baking dish. Place 3 lasagne sheets on top. Place the beetroot slices on the lasagne sheets, spread the beetroot purée over the beetroot slices. Scatter the cheese over the top.
Peel the squash, remove the seeds, cut into approx. 3 mm slices.
Place the lasagne sheets on the beetroot layer. Spread the bechamel sauce and squash slices over the top, and scatter cheese on top.
Place the lasagne sheets on the squash layer. Roughly chop the spinach, mix with the oil and salt. Mix 200 ml of the bechamel sauce with the spinach and spread over the lasagne sheets.
Place the lasagne sheets on the spinach layer, spread over the remaining bechamel sauce, scatter cheese and butter over the top.
Approx. 45 mins. in the centre of an oven preheated to 200°C.