Citrus isn't a New World fruit.

Both lemons and limes have origins in an older cultivar referred to simply as citron. There's, of course, some controversy in where they were first attested, with evidence of citrus trees from 2nd century B.C.

The earliest evidence of Citrus seeds comes from northern India, from the early 2nd millennium B.C. site of Sanghol in Punjab. (Pagnoux et. al, 2013)

Limes seem to have a slightly different origin, according to Nicolosi et. al circa 2000

The ancestral place of lime origin is also controversial, similar to that of other citrus species, but many researchers and historians believe that lime originated from South-east Asia around 4000 bc and its native home is the Indo-Malayan region (Nicolosi et al., 2000).

Romans were familiar with these fruits, as they were first attested in Dioscorides de Materia Medicis between A.D. 40-90. Even our old gastronomic pal Galen gives it a mention fewer than 100 years later.

The first description of the fruit is from Dioscorides (ca. A.D. 40–90): elongated shape, wrinkled and golden yellow skin, fragrant and similar to a pear (Mat. Med. 1, 115, 5). Galenus (Galen) (A.D. 129—ca. 200) describes it more precisely. The fruit is divided into three parts: the inner part, which contains the seeds and is acid; the flesh, which is juicy and refreshing; and the skin, which has ‘‘acrid oil’’ (Simp. Med 8, 19; De alimentorum facultatibus 2, 37) (Ku¨hn 1965).

Now once again, this is the citron they're talking about, which bares a stronger appearance to a lemon with its yellow hue. The sour lemon would take another millennium to be popularized in Italy, introduced by Arabs in the region, and also brought back as exotic fruits by crusaders.

After the crusades it was taken to Palestine and then finally spread to Mediterranean Europe (Cooper and Chapot, 1977; Eckert and Eaks, 1989).

As a symbol of the crusades, the near-East, and displays of wealth, ornamental lemon trees became an important symbol of conspicuous consumption.

Your question is difficult because the question is posited as if Italians were simply choosing one preference from all available citrus. In reality, different cultivars with different appearances were introduced at different times, with the majority of the ancient citrus bearing a bright golden hue.

As Italian lemon cultivation expanded and new, sour lemons were introduced by the Arabs (which were juicier and smoother in appearance), the bright, yellow lemon became visually entwined with Italian culture and began to be used in more and more of their foodways.

With the appearance of the citron already embedded in the cultural lexicon as something exotic, rare, and special, the process of signification had done its job. Sure you could eat one of those modern, green citruses, but the yellow citrus had a thousand years of historical precedent. The lemon was not just something to eat, but something to point to as a sign of your cultural savvy.

You can read more about the abundance of Italian citrus varieities in Gallesio's Traité du citrus (1811) that describes the appearance of pre-industrial varieties.

You can also read more about the process of mythologization and signification in Roland Barthes' "Mythologies"

Sources:

Nicolosi, E., Deng, Z.N., Gentile, A., Malfa, S.L., Ciotinella, G., and Tribulato, E. (2000) Citrus phylogeny and genetic origin of important species as investigated by molecular markers. Theoretical and Applied Genetics 100, 1155–1166.

Cooper, W.C. and Chapot, H. (1977) Fruit production with special emphasis on fruit for processing. In: Nagy, S., Shaw, P.E. and Veldhuis, M.K. (eds) Citrus Science and Technology, 1st edn, Vol 2. AVI Publishing Co., Westport, Connecticut, pp. 1–127

Eckert, J.W. and Eaks, I.L. (1989) Postharvest disorders and diseases of citrus fruits. In: Reuter, W., Calavan, E.C. and Carman, G.E. (eds) The Citrus Industry. Division of Agriculture and Natural Resources, University of California Press, Berkeley, California, pp. 179–260

Pagnoux, Clémence & Celant, Alessandra & Coubray, Sylvie & Fiorentino, Girolamo & Zech-Matterne, Véronique. (2013). The introduction of Citrus to Italy, with reference to the identification problems of seed remains. Vegetation History and Archaeobotany. 22. 10.1007/s00334-012-0389-4.

Barthes, Mythologies, 1957