Ground Yourself

It never ceases to amaze me how many people forget to keep their back foot flat on the floor when lunging (and that's not easy to say or type). I guess the reason a lot of people twist their foot over is because their lunge is more of a fall or lean than a thrust and they would argue that they are putting more into it. The truth is that without the foot being kept flat there will be not true power in the the lunge. There may be momentum but that is not the same as power. A proper lunge explodes from the back foot, which anchors the fencer as they push off. Keeping the back foot flat also means there is less tendency to fall forward. Next time you are fencing try putting your awareness into your feet. I often do this, particularly when fencing defensively as it gives me a greater sense of stability. Try gripping the floor through your shoes, it can give a great sense balance. (This also helps in other situations where you are nervous).
On a more practical side, make sure your fencing shoes are free of dust on the soles as this tends to accumulate and will mean you slip and slide more often. Just scraping them down the wall or rubbing them vigorously on the floor may remarkably improve your grip. I wouldn't recommend rubbing them on your socks like some fencers do, the grubby marks do not add to the appearance in my opinion!