Well, first of all, memory manipulation really should be priced higher because of how destructive it can be creatively.
Second, we run into the fact that events in creatures' lives can alter them greatly. Whether or not these actual events play out is irrelevant to how we reference them. I could, for example, implant a traumatic event of a disaster that occurred during kit-hood, then watch the subject reference that memory and react as if it were always there, so long as I weave it into the memories well enough. Once this happens, this cat will refer to that memory again, if it is relevant enough in his/her life, and possibly lead to a change in usual problem solving and mental consideration. A more fanon-related example would be if I had Lapisvision hypothetically gave Rangerstar a false memory of Gunslinger privately telling him how much he hated Riverclan and would be glad when Rangerstar died. (I don't plan on doing this though, it's just an example). When it comes time to pick a new deputy due to... let's just say a surprise missile attack, guess who now has less chances of being picked because of the memory Rangerstar would then remember and use to judge against?
Third, we consider the very basis of Behaviorism, which behavior and personality are assumed to be the result of learned behavior starting from birth and on. What Lapisvision currently seeks to do is practice whether or not injection of false memories to learn new behavior or altering of past memories to replace habits will be more efficient and ultimately powerful in changing a cat's learned behavior, depending on how much the cat in question will reference the memories. We know in the Warriors canon (specifically citing Cats of the Clans with the Starclan kits) that the spirit's form is dependent on the age and personality of the body at the time of departure, so it stands to reason that a cat's spirit could be directly altered by these factors in-fanon, so long as it is done thoroughly and carefully.
Of course, this only stands possible to a creative mind and genius in order to plan and execute in a massive scheme of epiphany stacked on epiphany. However, before you question me on how to do this, consider this...
Lapisvision can read Twoleg books and other materials, was in Twolegplace for two weeks on his return to deliver Sheeppaw's message (which he actually knew where all of the facilities he needed were, on account of numerous explorations when he was younger with his mate), was and has an above-average, if not genius intellect.
Too long; didn't read: This power is broken, and I'm going to use it.
Now, as for why Eagle, there are a few reasons. One being that somebody somewhere here stated that he/she wanted to plot will all of the cats in Riverclan. I don't remember who, exactly, but your name just sounds right.
Second, starting from an in-game perspective, because the foreign language is kind of a cute quirk that's also relatively innocent. Lapisvision knows this, and if he can succeed in replacing a kit's native language with Polish, then he stands closer to learning how to completely rebuild a cat into his fitting. The best part of it is that he can use Eagle's presence as an alibi if the other cats start to catch on ("Eagle was just around the nursery, talking to herself a lot, so the kits caught on.")
Third, Eagle is skilled as a warrior, and if anything can also pass one a battle move or two.
Fourth, because of the fact that Eagle is a warrior, she has quite a few moons on her. Lapisvision, in order to produce the most efficient results in his future rampage, needs to know the amount of experience and behaviors will yield the best results. A kit, for example, might be more of a mind to sculpt, but is part of a more impatient and rash group that may or may not take the behaviorist injections well enough to satisfy expectations. Meanwhile, though more of a challenge to fully remold, a warrior may or may not depend on memories of training in certain situations, and has plenty of other situations where a memory would be referenced (social events, clan meetings, etc...). Lapisvision, in order to produce the best possible rampage, will need to study Eagle's recent memories to see when she referenced her memories and how she did so, so that he can have data on at least one young warrior.
Too long; didn't read: because Eaglesoar fits pretty damn well.