It took nearly eight hours for the poison to be cleansed from Lex's body. He wasn't completely healed by the time that was done, but he was well enough that he exited the tube to complete some of his other tasks. During this previous expedition, though he had a sword, he had not ended up using it even once. He had practiced using it a little, but the matter of fact was that he was nowhere near competent enough to use it skillfully.
Heck, he had only been a cultivator less than a year, or a little more - he had lost track of time - but he had been so busy during that time that something like training methodically and systematically was impossible. He had gotten better with his gun, but only because his enhanced senses made using it simple. The amount of time he had trained was miniscule.
As such, for now at least, carrying such a weapon was not feasible for him. Perhaps later, when he had the time to train, he would come back to it. Now, though, he decided to go even simpler.
For those trying to recall what the Henali conventions were, they were first mentioned in Chapter 33 by Falak (Bastets attendant). The details of the convention were not stated, but it was hinted that it prevents higher leveled cultivators/civilizations from interfering in matters of those lower than them.