Why can't you change the fuel mixture mode in qualifying on the downhill lap? You can set the LEAN mode on the outhill lap and change it to STANDARD later. Such a change on the downhill lap would be...
Ideas
That's why the game has a [low fuel mode] that automatically activates when you run out of fuel. It slows the car down significantly, but it also means you can drive in this mode for an entire session (at a snail's pace) without entering the pit lane. Now that's UNREALISTIC!
My suggestion: Remove the low fuel mode. Allow switching to LEAN mode in qualifying on the pit lap (only when the fuel level shows LESS than 1 lap, e.g., from 0.9 or 0.8). This will allow you to enter the pit lane without drastically slowing down. However, when you run out of fuel, the car should stop and a RED FLAG should be displayed. Red flags should also be used in practice and qualifying. Of course, there should be a corresponding penalty for calling a red flag in qualifying. And that would be a REALISTIC solution!