Lag can definitely play a part in the problem and it can be really nasty if you start getting lag spikes while fighting some of the later bosses like the HM and EX primals.

If it is continuously happening, I would make sure that I have a good connection on my end. If you are on PS3 and connecting wirelessly, maybe try going wired.

As far as what you can do in game, learn the attack patterns and aoe attack so that you can predict and quickly react to them. Also follow the shortest path to get out of the aoe, for cone attacks it is often best to just run straight and through the boss.