Why is the Lewis structure of ozone important?

Why? Because it's a simple predictor of molecular shape.

The ozone molecule is ##O_3##, and each ##O## centre contributes 6 electrons to the valence shell.

A reasonable Lewis structure would be: ##O=O^(+)-O^(-)##. Because, around the central oxygen, there are 5 electrons (2 from the double bond, 1 from the single bond, and 2 from the lone pair), we assign this centre a positive charge, and of course we can assign each terminal oxygen a negative charge alternately by resonance.

Given the Lewis structure we predict by ##VSEPR## a bent molecule with ##/_O-O-O## ##<=## ##120""^@##. What do we find experimentally? A bent molecule with intermediate ##O-O## bonds; ##/_O-O-O## ##=## ##116.8""^@##.

Thus, by simply knowing how to draw a Lewis structure, counting the electrons, and using ##VSEPR##, we have predicted the structure of a gaseous molecule, which we can't see, but we can smell. I think that is pretty clever given the (short!) time we spent on the problem.