Lictors were Roman civil servants. They were recruited from the ranks of the Roman Plebeian class. Livy described them in the following terms:
Twenty-four lictors were all the retinue of the consuls, and even these were plebeians. Nothing was more contemptible or weaker, if there were any to contemn; it was every man's own imagination that made them great and awe-inspiring.
They were often former soldiers, and were also employed to carry out punishments. In return they received a received a fixed salary (of 600 sesterces at the beginning of the Empire, according to the Wikipedia page).
They would be unlikely to be punished for fleeing the mob in Rome (the histories that survive include many stories of people of all ranks having to flee the mob). However, they might lose their employment (since they were often personally chosen by the magistrate they were supposed to serve) and so also lose their sole source of income.
In fact, Livy recounts another case where a lictor confronted the mob:
... the consuls sent a lictor to him. The lictor was driven back. Whereupon, with a cry of “Shame!” the senators who were attending the consul rushed down from the tribunal to assist the lictor. But when the mob turned from the officer, whom they had merely prevented from arresting the man, and assailed the senators, the consuls intervened and checked the brawl, in which no stones had been thrown nor any weapons used, and there were more shouts and expressions of rage than hurts. The senate was convened in confusion ...
In that case, the lictor did not abandon his post, but the limits of the lictors when confronted by the mob were made abundantly clear. The limits of the Senate in the face of the mob were made equally clear.