The major difference between the Lewis dot structures and the Lewis line structures is that the latter uses lines to represent bonds. Each bond is a line. Each bond contains 2 electrons. Thus each line is two electrons. For instance:
This way a single bond is represented by a single line, double bond—with a double line, and a triple bond—with a triple line. While a higher order bonds are possible, quaternary bonds are a bit of an exotic type of a bond, but not unheard of. In organic chemistry, we do not work with anything higher order than a triple bond.
Lewis line structures also generally show the non-bonding spare electron pairs on atoms like oxygen or nitrogen. This is, however, not strictly speaking necessary. There are many “implicit” parts in organic structures and electron pairs are often among those. Thus, they are usually only shown when it is necessary.
Two ways of drawing Lewis line structures
There are two common ways how Lewis line structures are usually drawn: straight line and zig-zag.
While the both ways are, strictly speaking, correct, the zig-zag way is a generally preferred method for drawing the molecules because it closer represents the actual 3D structure of an organic molecule.
Drawing a full Lewis line structure is still a bit tedious though, thus we only use this method when it is essential to show every bond in the molecule (not all that often). Condensed structures are way more useful in this regard.