Continuing on what @Bryan said, lag on block break may be related to the server you're on (assuming you're on multiplayer). I recently had a similar issue on my server, about 1 second after block break to give the block. In my case, my server's cpu was pegged at 100% during this time. I scaled up to a bigger machine, and the problem has gone away. There could be other causes for this, I'm just pointing out what it was for me.