In verses 3-5 Jacob is recounting briefly the prophesied life of Christ, emphasizing the "iniquities" of the Jews that would cause them to crucify their Messiah. In addition to the necessary statement of fact, Jacob probably has other reasons for stressing the iniquities of the Jews. Traditionally, the Nephites emphasized the iniquities of the Jews as it related to their departure from Jerusalem, with the fall of Jerusalem the penalty for those iniquities. Against that background, Jacob has a believing audience in the capability of the Jews to crucify their savior, because they also were sinful enough to allow Jerusalem to be destroyed.
Jacob also has another thought in mind however, as his discourse is not aimed at blaming the Jews, but at highlighting the need for repentance in his current audience. He has set them up by reminding them first of the promise that came with obedience, and secondly with the prophecy that their children will fall away. Thus Jacob is pointing this sermon directly at his audience. In the previous day he rent his garments. Now he displays the iniquities of the Jews as an example of the iniquities and ultimate results his audience might be capable of bringing upon themselves.
Historical note: "Crucifixion was in use among the Egyptians (Gen. 40:19), the Carthaginians, the Persians (Esth. 7:10), the Assyrians, Scythians, Indians, Germans, and from the earliest times among the Greeks and Romans. Whether this mode of execution was known to the ancient Jews is a matter of dispute. Probably the Jews borrowed it from the Romans." (Smith's Bible Dictionary, 1970 p. 122)
While it may not have been practiced as a form of execution by the Jews until the Roman influence, the extent of the form of execution in surrounding cultures (and particularly Egypt) suggest that Jacob would have known what crucifixion was, and therefore is able to use that term without explanation. The noted close ties of Lehi and his family to Egypt make this the best possibility for their source of information about this form of execution.