Humans: Running would be Health, which isn’t a skill so you can use nature. There might be some edge cases where Boasting or Demanding can be used in a way that’s not persuasive or manipulative, but actually I’m having trouble thinking of them.
Elves: Singing isn’t covered by any skills. Remembering can be used for actually remembering something that happened to you, like remembering a pass-phrase or a sequence of numbers, which wouldn’t fall under Lore Master.
Dwarves: Delving might work, as long as it doesn’t easily fit under laborer. So if you’re just digging a ditch, no, but if you are mining a vein of ore, yes. Crafting is a maybe if it doesn’t fall under one of the existing craft skills, or if you decide not to take the craft skills since you already have all of them with your nature. Avenging a Grudge can be used in place of any Health or Will type tests as long as you have a grudge against your target.
Halfling: As mentioned, merriment. Riddling might also come up if Lore Master doesn’t apply, but it would have to be outside of a conflict…
Looks like it’s hardest to play the Low Nature game as a Halfling or Human and easiest as a Dwarf, particularly if you avoid picking up the craft related skills. Elves are somewhere in the middle.