There are a number of factors the left handed golfer needs to take into account when playing a shot from a downhill lie including stance, posture and swing path and angle of attack.
The first thing to understand is how the tilt of the ground will affect the stance and posture. The more severe the downhill hill, the more the left handed golfer will have to tilt their spine towards the target. Normally this would steepen the angle of attack on a flat lie. However, because the ground is tilted more towards the target, the angle of attack should follow the correct arc through the ball. This extra tilting of the spine will shift more body weight on to the front foot. This is almost unavoidable but left handed golfers should take as much care as possible to keep the weight distribution even between the feet. If too much weight is placed on the front foot at address, the natural motion of the body moving down the hill through impact could cause the golfer to lose their balance.
The downhill lie could also affect the swing path. On a normal shot from a flat lie, players should be looking to achieve an inside-to-square-to-inside swing path through the ball. When the lie becomes tilted towards the target it becomes much more difficult to achieve this swing path. A more consistent way to play this shot is to open the slice to the right slightly. This will produce a more out-to-in swing path and produce a more faded flight. Because the downhill lie will de-loft the club being used, the ball will fly lower than normal. Opening up the stance and allowing for a slight fade will also add a little more height to the shot.
As the slope becomes more severe slight alterations will have to be made to the posture, mostly in the knees. The spine angle should be maintained as normal unless the slope is also tilted more towards or away from the player.
As mentioned above, the angle of attack into the ball is vital to achieve successful strikes on a downhill lie. Most of the work will be done by altering the spine angle but attention must be paid to how the hands work the club. It is extremely tough to take a divot from a downhill hill. On a flat lie, the club should bottom out just after the ball, taking a crisp divot. With a downhill lie, the ground effectively drops away and leaves a space where the divot would normally be taken from. When swinging through the ball, players shouldn’t be tempted to try and lift the ball into the air but swing down the slope and try to strike down and through.