This short video highlights some of the modifications necesary to bolt a 4T80e transaxle to the LS4. This is not intended to be a step by step.

Few things not mentioned in the video to consider:

-When chosing a 4t80e, try to stay pre 99. Pre 99 models had a 3 switch manual pressure manifold identical in output to the 4l80e where as post 99 only had a 2 switch manifold.
-Converter bolt pattern on the 4t80e is 4 bolt square as opposed to 3 bolt triangular from the 4t65e. You will need to have your ls4 flexplate indexed and redrilled for this pattern.
-In the w-body chassis the complete engine/ transaxle package will need to move forward a minimum of 1" to clear the steering rack.
-Transmission cooler line fittings in the 4t80e case are male -6 AN o-ring.