for me, mirrorless is all about the evf, because for manual focusing use, evf blows away all dslr ovf options... and no, there isn't any lag with mirrorless:
"Bolstering the EVF, the NX1’s DRIMe V Image Processor cuts down lag time to just 0.005-seconds so that the EVF reflects the scene being shot in near real time, without delay."
Samsung Unveils its New Premium Camera, The NX1 | SAMSUNG UK
however, if you set the evf to reflect the exposure that you are taking, the framerate of the display can drop down, and get noisy as well, in poor lighting conditions... slow framerate essentially looks and behaves like lag.
if you want the evf to behave like a crippled ovf, that doesn't reflect the exposure of the picture that you are taking, you can set the evf up to do that, and then you won't see any framerate issues... but you'll have to resort to obsolete dslr functionality, like opening the lens up all the way in dark conditions, in order to set focus and such, then stop it back down... which introduces focus shift into the situation.
downsides to evf include the inability to display the full dynamic range of the picture being taken, despite the fact that you can see what the exposure will look like in the photo... this bugs some people, but i haven't found it to be much of a problem.
if you use an evf for high fps action shooting, you could see the evf black out between shots, which can be annoying... the few times that i've shot high fps with the a7r, i just kept panning the camera through the dark evf, and the framing stayed correct.
with mirrorless cameras you shouldn't have to do much if any front/back autofocus adjustments on the lenses... and you can shoot with just about any camera lens that's ever been made, which no dslr can do.