'on' means touching a surface or being supported by a surface. 'in' is used with the name of a container, place, or area to say where someone or something is according to the Longman Dictionary of Contemporary English.
If A is in B, it usually means that B contains or has A inside. B is bigger than A. For example, a country (A) in Africa (B).
If A is on B, it usually means that B supports A. B may or may not be bigger than A. For example, a book (A) on my hand (B).
Thus, 'on' is the right word. 'You can sit in my lap.' is very weird. It makes me feel that the lap is bigger than a person and is hollow inside so that the lap can contain a person.