A friend of mine posed an interesting question. He asks, at what angle does the lap no longer exist? Obviously, the best way to solve this question, is with science.
Someone suggested that the lap disappears as soon as it will no longer hold a dog. I thought to myself, this is actually a good specific example of a general idea we could use.
A lap is no longer a lap once it is incapable of holding a static load. There are several factors that play into this. Mainly, How much does the static load weigh, and what material (if any) is your clothing made of? Once those two things are accounted for, the maximum angle with which your lap may be without an object falling off can be found. I call this value, the Terminal Lapicity.
I am not aware of any tables of friction coefficients of clothing materials (thought I am positive there are some out there somewhere) But if anyone wishes to establish this table for me experimentally, you can find the coefficient of friction of each material by measuring the angle of the lap right before the object slides, and then taking the tangent of that angle.