Today I had an embarrassing experience when I sat to help my nephew learn Lewis' Dot Representation and realized that I actually don't get it at all. I have a physics background and always thought that the Lewis Structure in chemistry mimics the physical picture, but soon realized that it doesn't.
First of all, the "sockets" where the dots go on Lewis Diagrams do not correspond to actual physical orbitals. They are neither 4-fold symmetric, nor are equivalent (s-orbitals are spherically symmetric, p-orbitals are lobed, etc), so I couldn't give any explanation to my nephew what their physical interpretation is.
Also, I noticed that the rule for filling these "sockets" do not follow the Aufbau rule. For example, in the ground state of carbon, Nature first fills the $\ce{2s}$-orbital and just after that inserts an electron in two of the $\ce{2p}$-orbitals. In contrast, the rules of Lewis' Dot Representation say that C should have a single dot in each of its 4 "sockets", and just after they get exhausted, one starts pairing them. (I wonder how this principle explains compounds like methylene, in which carbon has its $\ce{2s}$-shell pair present... but anyway.)
All of this prompted me to ask, what is the story behind Lewis' Dot Structure and what goals Gilbert Lewis pursued when he introduced it? I guess if I learn this, I'll be able to explain its misleading features and not get embarrassed in front of a 14-year-old.