This situation takes a lot of confidence. A little practice would be good too. When we are this close we often want to use our chipping technique, but with deeper rough this would be the wrong selection. The heavy rough makes it difficult because the club will not have the velocity it needs to cut through this rough. Using a bigger swing with more velocity makes us nervous because if we happen to top the ball it will go well beyond the distance we need it to.
You need to select the correct technique, the right club and then commit to the swing. In this case you should select the pitch technique and the highest lofted club you have. Typically, this would be a sand wedge. Open the club up a little to create a little more loft and to allow the club to cut right through the rough. If you open it too much (especially with a lob wedge) you risk going right under the ball. When opening the clubface it will change the alignment right of the target (right hand golfers). Thus you will need to modify your set up to compensate for this change in direction.
Now select the pitch swing. This is a small version of the full swing where the club loads with some wrist hinge in the backswing and the follow through. The chip swing is a much smaller arch swing and resembles that of a putt swing with no wrist hinge.
Take a few practice swings on the slope to gauge rough and to prepare yourself to commit to this swing. Now go for it! Give yourself this situation near the practice green so you can experience this and get a sense of how this works. If it works without any practice, then you should go buy a lotto ticket.
Have a look at the video to get a better sense of how to accomplish this.