Question

Where is `"FeCl"_3` used? Is it a Lewis acid or base?

Answer 1

It’s not just about the “pairing” but which molecule can accept an electron pair or form and adduct.

Explanation:

Anhydrous iron(III) chloride is a fairly strong Lewis acid, and it is used as a catalyst in organic synthesis. Iron(III) chloride is a moderately strong Lewis acid, forming adducts with Lewis bases such as triphenylphosphine oxide, e.g. FeCl3(OPPh3)2 where Ph = phenyl.

Iron(III) chloride reacts with other chloride salts to give the yellow tetrahedral FeCl4− ion. Salts of FeCl4− in hydrochloric acid can be extracted into diethyl ether.
https://www.cs.mcgill.ca/~rwest/link-suggestion/wpcd_2008-09_augmented/wp/i/Iron%2528III%2529_chloride.htm

From http://chemwiki.ucdavis.edu/Physical_Chemistry/Acids_and_Bases/Acid/Lewis_Concept_of_Acids_and_Bases
Lewis Acids
Lewis acids accept an electron pair.

Lewis Acids are Electrophilic meaning that they are electron attracting. When bonding with a base the acid uses its lowest unoccupied molecular orbital or LUMO

Various species can act as Lewis acids. All cations are Lewis acids since they are able to accept electrons. (e.g., Cu2+, Fe2+, Fe3+)
An atom, ion, or molecule with an incomplete octet of electrons can act as an Lewis acid (e.g., BF3, AlF3).

Molecules where the central atom can have more than 8 valence shell electrons can be electron acceptors, and thus are classified as Lewis acids (e.g., SiBr4, SiF4).

Molecules that have multiple bonds between two atoms of different electronegativities (e.g., CO2, SO2)

Lewis Bases
Lewis Bases donate an electron pair.

Lewis Bases are Nucleophilic meaning that they “attack” a positive charge with their lone pair. They utilize the highest occupied molecular orbital or HOMO (see Fig. 2). An atom, ion, or molecule with a lone-pair of electrons can thus be a Lewis base. Each of the following anions can "give up" their electrons to an acid.  
Example: OH-, CN-, CH3COO-, :NH3, H2O:, CO: