Research in LW2 proceeds much the same way as in vanilla XCOM 2, but is expanded.
ADVENT Trooper autopsies require 20 corpses before they can be completed instantly. ADVENT Drone autopsies can never be completed instantly. All other research autopsies require 10 corpses or wrecks before they can be completed instantly. The check for instant completion is run after any research project is finished.
Comprehensive Tech Tree
Created by Reddit User exodusinfinite
The Basic Tech Tree 1.3 (without Item stats) is available here
The full Comprehensive Tech Tree 1.3 (including item stats) is available here