Lyle decided not to fully focus on either one of the two at the very end.
His fighting ability was very important and he couldn't sacrifice that just to study poisons as he knew that no matter how much he practiced the art of poison, he would never be able to reach the heights that Ilya had reached.
Ilya's ability itself was poison and he could conjure it from his body or the surroundings simply by using and manipulating mana. Poison was like an extension of his body and the power it had was directly connected to him, meaning that even without studying the art of poisons, Ilya would still have incredibly deadly poisons that could kill others.
Lyle, on the other hand, needed to study the art and use what Ilya had left in order to learn how to concoct poisons himself before being able to use them. From what little he had browsed through Ilya's many scrolls and short diaries, he learned that the man had actually even used most of the poisons on himself.
