1. "She didn't want to disturb her sleeping husband, so as usual, she took out a small pistol from the drawer to check on the animals." From this detail, if the murderer is Lise, it is impossible for him to know the details of the life of the Buick couple (couples can't talk about this topic), that is to say, if he plays a tape harassing animals, it may wake up the Buick couple, and if they go to see animals together, it is impossible for him to commit crimes. If the murderer was Lise, it would be impossible to use this technique.
Second, if Liz killed Mrs. Buick, then Mrs. Buick should have been led to the crime scene by a note in her pocket. But in fact, Mrs. Buick was awakened by other animals and rushed to the crime scene. Since Liz had an appointment with Mrs. Buick, why did she play a tape harassing animals to wake Mrs. Buick? Isn't this unnecessary?
3. If Lise is the murderer, he certainly won't leave a note as evidence: because it is impossible for a husband and wife to use such a note, which is evidence against them.
As a husband, he fully understands the details of his wife's work and rest. He can lure his wife to a certain place with the sound of animals, then kill her with the past and leave a suicide note to frame Ulysse. The motive of killing is to kill his wife after learning that she has committed adultery with her good friend and can't stand her betrayal.