that is for sure not normal.
i have an mhl adapter so when i get home i can test it. i use the media link adapter which is virtually no lag.
are you watching a file locally on your phone or are you streaming from, say, youtube?
doe this happen on any file you try to play?
if you are using , say, youtube app, are you on wifi or cellular?
can you try another display?
another hdmi cable? slower speed cables may also impact performance a bit.