I'm still going over names. Is it possible that 'laith' originated from the Gomish word 'laith¹', a noun meaning 'time, the course of time; (properly) lapse', thereby suggesting 'up time'? Could it imply rising to become the first king? Just a thought – maybe I'm reading too much into it.
On another note, I was thinking about 'Amon Darthir', and its etymology. The name might be a combination of the words 'dartha-', as suggested by elfdict.com, meaning 'to endure' or 'to last', and the latter being 'hîr', meaning 'lord'. This suggests that 'Amon Darthir' could be translated as 'Hill of the Enduring Lord'. This interpretation, which aligns with its location near the house of Húrin, symbolizes endurance or resilience, qualities that are strongly associated with Húrin's character and legacy. This thought came to mind as I pondered the significance of the mountain's name in relation to its surrounding lore.