2004 4l80e hot trans on hills

Ok so i put a lot of faith in my mechanic mr google but fact was as soon as the hrdolic lines busted on the output of the pump the engine and tranny temp dropped literally like a rock to normal. I saw the lines they where rusted completely and the pump blew, according to the mechanic, due to rust getting into the pump, plus lack of fluid(it was spraying all over the inside of the engine compartment) caused it to seize it. The coolant for the pump was not there they added an after market one. SO he said the coolent was being overheated by the hydrolic pump. Well that's what i remember. Since they did their work truck has been great except since it had a new pump with better pressure the rotten brake lines blew too. I do wish i had that 8.1l would make pulling my camper so much easier.