I found I couldn't open the white chest behind the bartender at the Gnawed Noble Tavern. So I went to Denerim to do some of the many tasks available there pre-Landsmeet. I decided to temporarily halt the Soldiers' Peak quest to see if after leveling up getting the highest level of lock-picking would allow me to pick this lock. While doing the Soldiers' Peak quest, I killed possessed Sofia and found a chest I couldn't open despite being on level 3 lock-picking. Despite being this advanced, I'm finding locked chests I can't open. I've prioritized the chest opening/lock-picking ability over combat skills and am already on the third level of this ability. In the last two play-throughs, I've used mods and done main quests in a different sequence.