93 civic with h22a swap tranny question

[h22slpr]

i am putting this engine into my civic dx my question to you is i bought a tranny with a lsd transmission my first question is what style of lsd is the tranny and the 2 lines coming off the diff are they for a oil cooler (my tranny is a 5 spd) do i have to run a oil cooler if so can i run it to the auxilarty cooler in the radiator (iam using the stock radiator or can i just put a piece of hose to the fittings to just loop the system please help my swap is going great i broke the tps sensor doing the install but i need help with just this