I got sick on my first lesson, which was quite a worry as I'd wanted to learn to fly for years, and I thought 'what if this happens every time?'.
I put it down to anxiety (through looking forward to it so much), took airsickness tablets for the next lesson, wore anti-sickness wrist bands, and checked that a bag was on board should the worst happen.
Been fine since, though still take the tablets, just to be on the safe side!