Even if your specs are well aboved the minimum, it is worth noting that the current state of XCOM 2 is spotty at best. The game mostly is all about the graphics card, if you have a Sandy Bridge i5 and up, you are good to go in the processing department. The lags are mostly due to the games graphical prowess (post-processing that is). If you are not running in 60 FPS, be sure to turn down the numerous graphical settings. The auto-detect graphic settings always put the maximum settings your rig can handle regardless of actual playable performance. Even if it means that your game will run on a single-digit framerate, then the game will choose the highest settings.
Screen Space Reflections is the first to go, they do look good, but if it means that your game runs better exponentially, then tick this off. Texture Filtering is the next graphical setting in the totem pole of performance impacting options. Anisotropic filtering heavily impacts the game, trillinear or billinear should be fine.
V-Sync is actually one of the settings that impacts the game, however, personally, I prefer no screen-tearing the high fps, if such is the strict choice. Turn off the V-Sync if screen-tearing is not the problem for your game. Otherwise, keep it on.
My rig is having problems with the game even though its not as graphically intense as some modern games (which the specs below can handle),
i7-3700 - CPU
GTX 760 4GB - VGA
8GB 1600Mhz - RAM
1TB 7200 RPM - HDD
I had all the graphical options in medium, no Screen Space Reflections, Trillinear Filtering for Texture Filtering, but V-Sync remaining. The game now runs at 60 FPS including the game engine cutscenes.