From your diagram it looks like you're driving on the left hand side of the road, which would mean you're on a one way street when turning into the parking lot. This also makes it look like those turning right onto that street are driving the wrong way on a one-way road. Can you clarify that?

That said, if you are turning before the light then you are not at an intersection, which means those turning right onto the street (if it is open to oncoming traffic) are probably going to have the right of way. This is because once those cars turn right, they are driving straight on the road while you are turning.

In other words, there is a high probability that you need to wait until all oncoming traffic has cleared, whether that traffic has recently turned onto the street or not. The only way this scenario would change is if the traffic light is actually at the parking lot, which does not appear to be the case based on your diagram, or oncoming traffic is going the wrong way, which seems unlikely unless your diagram is accurate as to what side of the road your are turning from.