I was in the middle of a sp battle on the test server and began taking ~5-10 seconds to respond to anything, then it booted me, and then it came back to the same lag, rejoining the battle and not putting anything down on the board. I refreshed again and then no lag, but now the lag's back... WITH A VENGEANCE!!!
It seems to be in and out, like a hiccuup, but with the hiccup being the normal speed and not the lag.
Since this doesn't seem related to any specific issue (rather than possibly server status, or general performance), I'll move this to support. In case you can pin down anything specific, as a possible cause I'll move it back.
I'm seeing lags of played cards hanging for about 5 seconds, and a similar delay after a character has moved while the placement message is displayed. It comes and goes within battles, both MP and SP. Probably not to the level Rook is experiencing.