In A Prosody Handbook, Karl Shapiro and Robert Beum claim:
The Latin iambus derives from a Greek word meaning "a cripple." The short syllable represents the lame foot, the long one descending with normal strength, perhaps with the added strength of the cane. (p. 35)
Shapiro, Karl, and Robert Beum. A Prosody Handbook. New York: Harper and Row, 1965.
Shapiro and Beum get a couple of things wrong. First, a person uses a cane to add strength to the lame foot, not the foot with normal strength. Second, as Peter Shor noted in a comment to your question, iambus does not come from cripple. The Online Etymology Dictionary provides this origin:
in prosody, 1570s (n.) "a foot of two syllables, the first short or unaccented, the second long or accented;" 1580s (adj.), "pertaining to or employing iambs," from Late Latin iambicus, from Greek iambikos, from iambos "metrical foot of one unaccented followed by one accented syllable; an iambic verse or poem," traditionally said to be from iaptein "to assail, attack" (in words), literally "to put forth, send forth" (in reference to missiles, etc.), but Beekes says "doubtless of Pre-Greek origin."
Beekes here refers to the Dutch linguist Robert S. P. Beekes. Wiktionary also mentions the Pre-Greek origins of the word:
Probably of Pre-Greek substrate (Illyrian/Phrygian) origin; the OED suggests a derivation from ἰάπτω (iáptō, “to assail, attack verbally”), literally "send forth", cognate with ἵημι (híēmi, “I throw, hurl”), as iambic verse was first used by satirists, but this could just be folk etymology.
It has also been suggested that the term is related to the minor goddess Iambe:
Iambe (Greek: Ἰάμβη) in Greek mythology was a Thracian woman, daughter of Pan and Echo, granddaughter of Hermes, and a servant of Metaneira, the wife of Hippothoon. Others call her a slave of Celeus, king of Eleusis. The extravagant hilarity displayed at the festivals of Demeter in Attica was traced to her, for it is said that when Demeter, in her wanderings in search of her daughter, arrived in Attica, Iambe cheered the mournful goddess with her jokes (Horn. Hymn, in Cer. 202; Apollod. i. 5. § 1; Diod. v. 4; Phot. BibL Cod. 239. p. 319, ed. Bekker; Schol. ad Nicand. Aleodph, 134.) She was believed to have given the name to iambic poetry, for some said that she hanged herself in consequence of the cutting speeches in which she had indulged, and others that she had cheered Demeter by a dance in the Iambic metre.
While the origins of the terms are uncertain, it is true that the iambus was a genre of Greek invective poetry. Since it was insulting in nature, it tended to use simple metrical forms close to natural speech rhythms. It defaulted, therefore, to iambic meter, which then as now was considered closest to natural speech—cf. the quote from the Princeton Encyclopedia in the answer your question links to. By association with the genre, the metrical foot began to be called iambus as well.
Shapiro and Beum conflate this term with choliambus, which does translate to limping iamb. The Merriam-Webster definition of choliamb provides this etymology:
Late Latin choliambus, from Greek choliambos, from chōlos lame + iambos iamb.
A choliamb is a satiric poem that has six feet to the line, with the last foot being a spondee or a trochee rather than an iamb. Hipponax, the originator of this metrical form, apparently chose this imperfect meter to symbolize human imperfections. The term "limping" was chosen because each line ends awkwardly and heavily on the wrong foot.
When I wrote the answer that your question asks about, I took Shapiro and Beum's mistaken etymology of iambus as correct; it was only in researching this answer, and after seeing Peter Shor's comment, that I realized it was wrong. I have edited the previous answer to rectify the mistake.