This is basically the result of an unfortunate incident a year or two ago which resulted in a member writing off their GT-R at lakeside. It was the first time they had ever driven their car in any situation other than on the street, they lost it and were unable to catch it, and went into the wall.
NO ONE wants a repeat of that, so this rule was brought in to help minimise the risk. It's not about the fact that QR is flat and lakeside has hills, it's more about the amount of run off area (and also the width of the track / proximity to other cars). If you have an off at lakeside, there's about a 95% chance that it's going to end in a bent car. At QR, theres about a 95% chance you'll have brown trousers but otherwise be OK. That's the difference.
Of course, if people drive happy laps at an appropriate pace (ie, no where near the limit of the car) it wouldn't be an issue. But for first time / inexeperienced drivers sometimes the fact they are on a race track gets the better of them and the red mist comes down. And some people are just d*ckheads.
So, the "QR first" rule acheives 2 things:
1) It allows inexeperienced drivers to get a tast of a race track / happy laps in a lower risk environment than lakeside.
2) It allows the exec to observe these drivers and make sure the ones that drive like knobs don't come back.
Allowances can be made if one/some of the exec know that you are an experienced driver and not a d*ckhead, but they're not going to just take your word for it.
The club runs plenty of QR happy laps so it's not really a big issue to get yourself to one of them first.