Back when I was working for a lightning company we had a list of interesting research questions. On top of my head one of the things were routing fees.
So what would be interesting to know is how much did fees rise in the last year, what is the distribution (for instance how much more do top routing nodes charge in comparison to other nodes) and whether there is any correlation between bitcoin network transaction costs and fee schedules on lightning.
Another pain point (at least for me as a hobbyist) are minimum channel sizes. We tried to measure them by trying to connect to every node and deduce from error replies what the minimum channe size is and show that through an explorer. An open-source tool for that or even using that as a consideration with autopilot mode would be great.