What's the intended purpose of Lethal Dose?
Literally *nobody* builds arena teams around poison. Incinerate, at least, provides an interesting utility effect with the built-in destroy mechanism - it could perhaps make some champs like Drexthar or Tyrant more usable in arena.
But doubling poison damage and allowing it some degree of RES pierce? You could quadruple the poison damage, and it still wouldn't be usable.