Yes, but most consider that to be a spurious document as well, and for good reason.
Though perhaps thought spurious, due to the fact that - “No Governor of Jerusalem; no Procurator of Judea is known to have been called Lentulus.” But Lentulus was a consul it appears, so he need not be either a notable Governor nor Procurator within the province to provide such information to Tiberias - as the consul (likely a suffect consul) the office would have been held for perhaps a half years time in those days.