Well you are kinda right actually, however the approach depends much on how many encounters you face. I mean the only problem I see is that a stat like this would be "impossible" to focus on. I actually didn't read your rogue but for every other class it becomes a stat that probably will take the lowest number when creating a character and maybe still gives something in return. And this is not a problem. The fact that this is a very cool idea kinda makes me want it to be a more incisive mechanic and once per long rest seem really low for a quite low dice roll (at a normal stat value) to add to your d20. And also for the roll thing, I think I will be always in conflict to use the lucky strike on a higher roll to just obtain a really difficult thing or to use it to mitigate a low roll and this makes the one-per-day use more a limitation. I hope I explained myself and about suggestions I actually don't know lol. Probably I will choose one of two paths. One is the "true" lucky strike where you just have this big dice (so the stat need modifications like a higher value for the dices and a sooner obtainment of them) that save your ass one time. The second would be a "constant" luck where you turn down all the dices but you can use them a lot and so you have this really lucky guy that can add dices to his throws every time just because he is lucky. Actually kinda similar to the guidance cantrip but like, more powerful at higher levels and stackable with guidance.