Bobbin lace is worked on a lace pillow, and is sometimes incorrectly called pillow lace.
However, the lace making pillow is traditionally a cotton covered horsehair pillow that is balanced on the knees and is large enough to hold both the work and the bobbins. Some of these cushions are almost solid mounds, others are more solid on top but soft underneath with a squishy filling that settles into the lap; so long as the lace maker can easily reach the work, the rest is personal preference.
Larger pieces of work need to be worked from a low table as the work past a certain point, becomes too large to sit comfortably on the knees.