Giolito, not Lugo, had a 3.79 ERA with the White Sox for 121IP, which is fairly respectable. Then he was traded (and waived) and from his break on, posted a 6.96 ERA over 53.1 IP.
In his first start with the Angels and his first SS tart with Cleveland, Giolito combined for 6.2 IP and 18 earned runs! . Who are these idiot managers leaving him in to give up 9 ER in 3IP? Without those two outings, his ERA post-trade would have been 4.89.