I can't tell you very much about Giacomo Colonna, but I can talk about the Letter of Lentulus.

The Colonna family is a fairly famous and powerful family in Italian history, particularly through the middle ages. Giovanni Colonna (1295–1348) was a cardinal, and a friend of the humanist Petrarchy.

The provenance that associates the letter with the Colonna family occurs in copy of the text in a 15th century collection of theological works, and states:

explicit epistola Iacobi de Clumpna, anno domini 1421, reperta in annalibus Romae, in libro antiquissimo in Capitolio, doct. domino Patriarchae Constantinopolitano.

(Cora Lutz. "The Letter of Lentulus Describing Christ." The Yale University Gazette. Vol. 50, Issue 2, 1975. p93)

So the text is found in a copy of the Annals of Rome, in 1421, by Giacomo (or Jacopo).

This also suggests that the letter was originally in Greek, and translated by a humanist.

The letter presents itself as from Publius Lentulus, to the Roman Senate and People, describing Jesus' physical appearance.

The letter's authenticity has been criticised on a number of fronts. Firstly, that there was no Publius Lentulus as governor of Judea. Prior to Pontius Pilte, the governor between 15-26 AD would have been Valerius Gratus.

This is not fatal though, as several persons named Lentulus were consuls in the period, and could have been the person in question.

More problematic, though, is that if this Lentulus was procurator of Syria, they would have written to the emperor, not the Senate, because Syria was an imperial province.

The main critique is that the language represents certain Christian and semitic turns of phrases that would be out of place for someone writing while Jesus was alive. These include "Jesus Christ", which even by the New Testament is still 'emerging' as a standard way to refer to Jesus. (the NT authors use "Jesus", "the Christ", "Christ Jesus" and "Jesus Christ", varyingly. the set phrase "Jesus Christ" which we are familiar with has not become the default expression yet). In any case, even the disciples do not refer to Jesus as "Jesus Christ", so it's anachronistic that Lentulus would.

Similarly, "prophet of truth" and "sons of men" are Hebraic idioms. They are not the kinds of things you would write unless your speech were influenced by Hebrew, and "sons of men" in particular would be an odd turn of phrase in Latin (or Greek).

There are, not exactly direct sources, but certainly earlier physical descriptions of Jesus. In the 14th century Ecclesiastical History of Nicephorus Callistus, the 8th century depiction in John of Damascus' Epistola ad Theophilum.

Lastly, I would say that there's a whole body of secondary literature about physical depictions of figures in antiquity, which discusses whether they are reliable, or whether they are intended to portray certain physical characteristics because they are associated with life and/or psychological traits.