The main two lap desk designs are those with a cushioned base that rests directly on your lap and those with legs that spread to either side. There are also some designs that rest on the floor like a portable table you can set up in front of whatever chair you want to use.
For those who want the most flexibility in seating arrangement, a lap tray with cushion can provide that versatility. You can use it on a couch, in bed or in an office chair if you want to put your feet up for a while. The design is popular for laptop PC gaming.
Meanwhile, lap desks with legs are well suited for places where you will be sitting on a stable surface with ample room to either side, like a firm sofa or mattress. If you stay up late writing on your laptop in bed, a laptop stand for beds may be exactly what you need.