I know that Lidl do not have an online store in most countries but they surely buy those tools from somewhere. Does that manufacturer or someone else related to them run a Parkside tools online shop where I can buy tools, accessories and parts in a single place without having to wait weeks or months for things to come back into stock in the supermarket?
I think part of the reason Lidl can sell the Parkside tools so cheaply is that they buy a huge bulk order all at once and they can sell all of those items very quick. If there were a parkside tools online shop, you would lose that model and prices would likely go up. If you could buy a jigsaw or something whenever you needed it, people wouldn't buy them so quickly and stock would be sitting around.
In saying that, it is possible to buy a large range of Parkside tools from Amazon but the prices are considerably higher than what you would pay if they come into stores. There are some stores for Kompernass and Grizzly tools that you can buy some parts and tools but they are based in Germany so you may end up paying a bit for shipping.