The company was last year stripped of the right to keep the brick's three-dimensional 2x4 shape as its EU trademark, after a challenge from Mega Brands.
The EU's trademark office, OHIM, granted Lego the legal right to the shape in 1999, but then agreed with Mega Bloks' case that a brick was a functional, technical shape which could not be owned by any one company.
Lego has already lost one courtroom bid to win the rights back, and its lawyers return to the European Court of First Instance in Luxembourg again on Tuesday.
They will argue that Lego brick design contains characteristics that set it apart from others - such as the design and size of the studs on top of the bricks.
The company is challenging the previous OHIM decision, upheld by judges, that functional shapes, such as a brick or any other "industrial design" must be excluded from trade mark protection.
Otherwise, the court argued, one company would have a monopoly on a basic shape which could be deemed to be "necessary to obtain a technical result"
Lego claims that competitors do not need to copy the shape of the Lego brick to achieve the same "technical solution", and that most consumers identify its studded brick as the company's brand.