Thanks for the additional information. It is helpful.
I'm sure you have heard that dogs are pack animals. Animals in packs often behave differently than dogs on their own. Likely Blue (I had a rottie named blue moon) didn't have any cause to act aggressive before lucky came. Once Lucky came, he felt that he had to show Lucky that he was the alpha of the pack. The alpha has privileges such as getting attention first, fed first, etc but it also comes with certain responsibilities too such as protecting their territory and other pack members. So it is possible when Kuma came to visit, Blue was showing Lucky that he was boss and when Lucky showed aggressive behavior toward Kuma, Blue did his duty and protected Lucky.
Since Blue is older, larger and already lived with you, he should have been the alpha. However, Pnschers are often very dominant as a breed regardless of their size so it is possible that Lucky became the alpha. In that case, Blue would be following the alpha's lead. Lucky would be leary of all larger dogs and possibly aggressive first to help keep other dogs away.
Now on to how to correct the behavior. The most effective method is having both dogs obedience trained. What obedience training accomplishes is that the dogs see you as the ultimate boss and learn to look to you as to how they should react around other dogs. It isn't an overnight fix but each time a dog obeys a command even if it is for the tiny hot dog sliver treats, they become a bit more submissive to you and then see you as the decision maker and protector. Of course you have to protect them meaning you will need to step between them and any potential threat.
The following site is helpful in helping owners train their dog. Be sure and click on the link to the page on obedience at the bottom. and links on subsequent pages leading to detailed instructions.
Training works best if you train at least 30 minutes a day (two 15 minute sessions). I would start making your dog work via the Nothing in life is free program (NILF). It is outlined below.
Now once you think you have them trained, I would then enroll them in a class to finish their training around other dogs in a controlled atmosphere like a class where everyone is focused on their dog and all dogs are on leashes with their owners.
In addition when you walk, you should not tense up or pull the dogs back when you see another dog approach. When you do, the dog feels your worry and thinks you are worried about the other dog and not them attacking. As a result they go ahead and become protective of you. So it is very important that you remain calm when they are on leash and not tense up.
I would restart you walks again and might consider walking them separately so you can work on their behavior apart from one another first. It will also help you determine if indeed Lucky is the catalyst for the behavior. This will also allow you to work with Lucky one on one easier.
You will need to get both of them walking fairly well on leash first before working with them again together. They may indeed revert back to the old behavior when together but then you focus on letting them know what behavior is unacceptable with low toned NO reprimands and using the treats to reward desired behavior. Keep the treats paper thin so they don't get filled up.
The BAT method may be helpful as well. REad about that below.
You should also learn body language so you can see if the other dogs or tey are transmitting aggression or dominance with their body posture. Read more on this here:
I am not a fan of dog parks. Too often a normal happy go lucky adjusted dog will go to a park and be fine until another aggressive dog attacks them. At that point they start feeling like they need to be aggressive first to prevent dogs from even getting close enough to attack them. I find it is better to find people with similar sized dogs of the opposite sex to be playmates on a weekly basis. Now you might find a smaller female as a playmate for Lucky and see if Kuma and Blue will regain their old relationship if Lucky is contained during Kumas next visit. Often once the relationship has turned aggressive, it needs a lot of work to repair.
I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have . If you do find this helpful, please take this opportunity to rate my answer positively so I am compensated for my time.