Yep, the handbrake cable on an LT77 is rod actuated on the box, whereas the R380 is cable actuated all the way into the box, so you will need the R380 cable. The crossmember will fit, but it is easier to use the R380 crossmember.
The speedo drive either needs to be swapped for the LT77 one, or use an R380 speedo cable. Either way will work.