Acid-Base definitions
In this post, we will go over the key aspects, reactions of Lewis Acids and Bases, and their relation to other chemical reactions. Before doing that, let’s do a quick recap of acid-base definitions in general.
The first theory for classifying acids and bases was developed by Arrhenius in the 19th century. According to this theory, acids produce protons in aqueous solutions and bases produce Hydroxide ions.

The problem with the Arrhenius theory is evident when some molecules react with acids and therefore act as bases, but they are not hydroxides. For example, the baking soda (NaHCO3) is a base and reacts with acids:

Because of this restriction, the Brønsted-Lowry theory was suggested as a broader definition of acids and bases. It states that acids are proton donors and bases are proton acceptors.
For example:

Notice that the bases are not restricted to hydroxides only. Any species that can accept (react with) a proton, including but not limited to the –OH are bases.
Lewis Acids and Bases
Gilbert Newton Lewis (the same Lewis who is behind the electron-dot formulas) suggested an even more general way of classifying acids and bases.
A Lewis acid is an electron pair acceptor.
A Lewis base is an electron pair donor.
For example:

What is different compared with the Arrhenius and Brønsted approaches is that Lewis took the opposite view, and instead of focusing on the proton, he looked from the perspective of electrons. The electron flow shows that the species giving the electrons are the Lewis bases, and the ones accepting them are the Lewis acids.

Let’s try to understand what this and the Brønsted acid-base theory have in common. You can think about it this way: protons are positively charged particles, and hydroxides are negatively charged. Therefore, you can visualize acids as “+” and bases as “-“.

Now, the Lewis bases donate/provide a lone pair(s) of electrons, which is what makes them bases. And if you think about any other base like –OH or the carbonate, which we classified under the Arrhenius and Brønsted theories, these also attack the proton with a lone pair. So, even if there is no formal charge on the base, it is still a species with high electron density, and we can look at it as a “-“ unit regardless if it is Brønsted or Lewis base.
Lewis Bases
Any base must have at least one lone pair or an electron pair in a π bond. That is why all bases are Lewis bases, but not every Lewis base can be classified as a Brønsted base since, by definition, Brønsted base is a proton acceptor.

However, conventionally, the term base is used to describe a compound that reacts with a proton, and only if there is no proton involved, we classify it as a Lewis base.
Lewis Acids
Similarly, the Lewis acid must be able to accept a lone pair, which is what protons do. However, the Lewis acids are not restricted to protons only. For example, boron is a common Lewis acid since it lacks an octet and has a vacant p orbital, which it uses to accept a lone pair and thus serves as a Lewis acid:

So, any Lewis acid is an electron acceptor; therefore, any Brønsted acid is a Lewis acid. However, not every Lewis acid is a Brønsted acid since the Brønsted theory restricts the acids to proton donors only.
To distinguish between those, the term acid refers to any proton-donating compound, and Lewis acid refers to the acids that are nonproton-donating.
Other common Lewis acids are AlCl3, Fe and Zn salts, and transition metals in general.
Lewis Acid-Base reactions
The Lewis Acid-Base definition is so broad that most (at least a very large group) organic reactions can be looked at as Lewis-Acid base reactions, and the reacting species as acids and bases. Think about this: any chemical reaction involves electrons flowing from one species to another. That’s what we show with curved arrows, and based on the Lewis theory, we can always classify the electron donor as a Lewis base and the electron acceptor as an acid.
For example, because Lewis acids are electron-deficient, they are also called electrophiles. And the Lewis bases are also called nucleophiles since they are electron-rich. The following reaction can be viewed as a Lewis acid-base reaction:

However, more often it will be viewed as a reaction between a nucleophile and an electrophile, which are discussed in a large class of nucleophilic substitution reactions.
In some Lewis acid-base reactions, bonds are broken new ones are formed:

The double bond acts as a Lewis base since it donates the electrons, and the HCl is the acid by any definition. And here again, this reaction will be most often referred to as an addition reaction to an alkene, even though it still falls under the Lewis acid-base category.
