I went to the local home improvement store and got a wooden plate in 85 cm. That would give the LEGO table approx. 15cm of additional room to hold LEGO bricks. Additionally I got the wooden edge pieces in 5cm to be as high as the LACK table.
Now with cuts at the place of the LACK legs you can just move the plate under the table. I glued it to the LACK table and fixed it with brackets. The edge pieces were doweled. Finally I painted it and glued the LEGO plate on the table. Ensure that you use solvent-free glue and paint, as it is a toy!