My 16GB version was returned because of this. The lag was so bad. The lockscreen almost always never worked. My phone had to be factory reset about 5 times. It started off great, then the more apps you would add, the worse the lag got. Others have reported exchanging their S4's for various reasons and reported absolutely no lag. Very early adapters could have been plagued by some defective hardware. Anyway, do you guys think the 32GB version will have lag?