title_body: By what means might the roots "let" and "ly" mean the same thing in a naturalistic conlang?
upvoted_answer: It is a two-step process, and both steps are very natural and frequently encountered in natural languages. The steps may occur in the other order as well, but the order here deems more common to me.
  
  
  Loss of the final stop let -> le. This occurs very often, French is a prominent example of this because the final stops are preserved in writing, but lost in pronunciation (with some exceptions when there is a following vowel).
  A vowel shift le -> li, in this case a raising. Again, this step is very natural because /e/ and /i/ are neighbouring vowels in the vowel diagram.
  
  
  These two steps use your assumption that let is the older form that evolves into ly. A more sophisticated construction could assume a common ancestor for both forms, e.g., lit that evolves to li by the loss of the final consonant and to let by lowering the vowel.
  
  EDIT: As you are generally interested in sound laws, there is a resource named Index Diachronica that lists a lot of sound changes collected from many sources.