What makes something a lewis acid or a lewis base?

Gilbert Lewis's definition hinges on donation or acceptance of electrons. The Lewis definition says that an acid accepts electrons and a base donates electrons.

The way I remember which is which is by associating Lewis bases with Brønsted-Lowry bases, and Lewis acids with Brønsted-Lowry acids---whenever a proton transfer is involved.

I find Brønsted-Lowry (BL) acids/bases to be easier to remember; BL acids donate protons. Naturally you would expect a general acid #"HA"# or #"BH"^(+)# to have a proton to donate, so that fits in nicely.

As a result, I tend to associate the BL acid with being a Lewis acid as well, because a BL acid will usually have to accept electrons in order to donate protons.

We can see that in the following reaction:

#"NH"_4^(+) + "OH"^(-)(aq) -> "NH"_3 + "H"_2"O"#

Alternatively, a reaction mechanism depicting it shows:

Ammonium (#"NH"_4^(+)#) has a proton to donate, so it is a BL acid, but it has to accept electrons from the hydroxide (#"OH"^(-)#) oxygen first before it is willing to do so, so it is also a Lewis acid.

Hydroxide donated the electrons, which is the opposite behavior to a Lewis acid, so it must be a Lewis base (and since it acquires a proton, it is also a BL base!).

What then results is the formation of ammonium's conjugate base, #"NH"_3#, and hydroxide's conjugate acid, #"H"_2"O"#.

(Based on the pKas of ammonium and water, the equilibrium is heavily favored towards ammonia and water, which is a convenient way of utilizing ammonia in lab!)