I have drunk water after 2pm and it doesn't seem to cause any problems. As long as you take the olive oil and lemon juice on an empty stomach you should be okay.
I have also had a few flushes where I threw up. I found that using grapefruit juice instead of lemon juice stopped this from happening (although I might have vomited because I was dehydrated and not as a result of the lemon juice).
Some flush protocols say that you should not drink anything for 30 min before drinking the olive oil and lemon juice, but I would say give it about 60 min just to be on the safe side.