Lewis Approach:
The Lewis approach, also known as the Lewis dot structure or electron dot structure, is a method used to represent the valence electrons of an atom in a molecule or an ion. It was proposed by Gilbert N. Lewis in 1916. The approach allows us to understand the bonding and electronic arrangement in a molecule.

Octet Rule:
The octet rule is a fundamental concept in chemistry that states that atoms tend to gain, lose, or share electrons in order to achieve a stable electron configuration of eight electrons in their valence shell. This stable arrangement is similar to the noble gases, which have completely filled valence shells.

Stable Electronic Arrangement:
When atoms are linked by chemical bonds, they can achieve a stable octet by either gaining, losing, or sharing electrons. This stable electronic arrangement is energetically favorable and makes the molecule more stable.

Explanation:
The Lewis approach is associated with the octet rule because it helps us understand how atoms achieve the stable octet arrangement. In the Lewis approach, the valence electrons of an atom are represented as dots around the atomic symbol. Each dot represents one valence electron.

Steps to Draw Lewis Dot Structures:
1. Determine the total number of valence electrons for each atom in the molecule.
2. Determine the central atom (usually the least electronegative atom) and arrange the remaining atoms around it.
3. Connect the atoms using single bonds.
4. Distribute the remaining electrons around the atoms to satisfy the octet rule. Place electrons as lone pairs on the atoms or as multiple bonds if needed.
5. Calculate the formal charges on each atom to ensure that the overall charge of the molecule is balanced.
6. Check if all atoms have achieved the stable octet arrangement. If not, rearrange the electrons or atoms to satisfy the octet rule.

Example:
Let's take the example of the molecule methane (CH4) to understand how the Lewis approach helps achieve a stable octet:
1. Carbon has 4 valence electrons, and hydrogen has 1 valence electron each. The total number of valence electrons is 4 (carbon) + 4 (hydrogen) = 8.
2. Carbon is the central atom, and hydrogen atoms are arranged around it.
3. Carbon forms single bonds with all four hydrogen atoms.
4. Carbon has used 4 electrons for bonding, and hydrogen atoms have used 1 electron each. The remaining 4 electrons are distributed as lone pairs on the carbon atom.
5. The formal charge on carbon is 0, and all atoms have achieved a stable octet arrangement.
6. The Lewis dot structure of methane is represented as: C with four dots around it (representing the lone pairs) and four H atoms connected to carbon with a single bond.

Conclusion:
In conclusion, the Lewis approach is associated with the octet rule because it helps us understand how atoms achieve a stable octet arrangement by gaining, losing, or sharing electrons. This approach allows us to draw Lewis dot structures, which represent the valence electrons and bonding in a molecule. The stable octet arrangement is energetically favorable and makes the molecule more stable.