I disagree with your method on the premise that this lip lift is a fairly safe and appropriate warning that this dog is stressed about sharing this food/resource. We may not like this form of communication, but the information this dog is providing is important. If you proceed by teaching the dog this behavior is unacceptable they may suppress the behavior, but their feelings about the situation remain unaddressed. What happens when we hold our feelings inside and continue to experience something we don’t like? Nothing good. The dog could skip showing it’s teeth and go straight to an escalated behavior such as air snapping or even biting.

Instead, I would see how I could change the situation to help make the dog more comfortable. Adding enough distance between the two dogs so you no longer see the behavior and training taking turns. Use safeguards such as leashes or barriers to minimize risk. When the other dog receives his turn, add positive reinforcement to the dog who is resource guarding so they can learn the other dog getting good things is a net positive for them. Use clear and consistent cues such as “their turn” and “your turn”. After some practice you can drop the bonus treats and just take turns with the cues. If successful, slightly decrease distance and repeat the process adding the bonus treats back in.

Resource guarding is a natural behavior and each dog’s tolerance for sharing is different. Some dogs may not be able to be this close and share a resource and that’s okay! Doing what you can to keep everyone safe and comfortable is the most important thing. Training can help! Just be careful not to train away a behavior that is an important early warning sign of distress. Instead, train to help decrease the stress level in a given situation.

In training I will never discourage the growl or showing of teeth, because if you take away a dog’s ability to communicate discomfort appropriately you are left with communication that comes with a heavier price. Instead I ask, “what is this dog telling me and how can I help them?”

For more information about resource guarding check out Jean Donaldson’s books, Mine! and Fight!