Most platformers have it, why not here? Sure it’s impossible to run the entire game lumless but surely something close to it
That sounds more like a score style challenge run than a time based speedrun. You're more than welcome to attempt this if you're interested, but I don't see the value in having a speedrun leaderboard for it.
A few others and I did this a while ago without teensies, I don't think every level is at the absolute minimum so you can try to lower any of the scores we have. https://docs.google.com/document/d/1xMU4p-Y3Q-aF0KdTL1HFfe0Jpr5rSaQ5n5BroV1MpH0/edit
You say we can get close to 0 lums. Actually, the teensies brings you lums,, so do the awesomness achievements and the endings of some levels. I never tried a minimal lums percent but i dont think you can get under 5000 lums.