
Data: Evidence, info, input, knowledge.
Lore: Belief, custom, adage, superstition, mythology, tale.
Data’s brother Lore is not real, it's just Data running a corrupted operating system.
Throughout the article I will be referring to Data and Lore as the Data OS (operating system) and the Lore OS to help with clarity.
The Lore OS has some mild tells, the name change into Lore, a common schizophrenic trait, the extreme emotional displays and outbursts, differing speech patterns like the use of language contractions, and even a facial tic that resembles a glitch in the motor controls. Notice however there is no difference in physical attributes whatsoever. Dr. Soong built the exact same model a second time? I don't think so. It would be extremely confusing to himself and the villagers.
When the enterprise visits the abandoned colony on Omicron Theta where Dr. Noonien Soong invented Data, they find another batch of body parts that is disassembled. The exact quote from Data at this discovery is "Can this be another me?" Holding up the mask of Lore, Geordie LaForge says, “Data, it’s you.”
They are hiding it in plain sight, right at the beginning. This is referred to as steganography, something used often in movies and novels to foreshadow an event or twist at the end of the movie.
Also, Dr. Soong building a new identical android, just to take apart the old one is nonsensical. If you have a software problem, you wipe the software and reinstall, you don't build all new parts.
No, what really happened is that Dr. Soong pulled out the hard drive and the crew found it and reintegrated the code into the android's positronic net. The intended purpose is that it would just add to his memories of what happened on the colony. However, it reinstalled the Lore OS unintentionally.
From then on the show depicts Data and Lore as separate androids. This is just a theatrical way of showing two sides of the same character. This is done enough in movies (Fight Club, A Beautiful Mind, Six Sense) that I don’t feel it’s necessary to go into great detail.

We’ve seen throughout the series Data become numerous other foreign personalities against his permission and will. The most noticeable one being in the episode entitled “Schizoid Man” where Dr. Graves overrode the consciousness of Data, this left Data OS unable to move, speak or think in any way, just like the Lore OS.
Most of the episode has both of them dialoguing throughout the ship ALONE, which further proves the point of a false character. There is an unspoken rule to limit the interactions of the false character with the unaffected characters because it would cause a contradiction, sixth sense for instance never allows Bruce Willis to touch anything.
The notable exception is Wesley Crusher. Wesley is a very unique wildcard in the series. He always notices out of the box realities, such as the Ferengi mind control game and the travelor's method of super warp drive. He can see the Lore OS and thus interact with it knowingly from the very beginning.
Data warns Lore to not underestimate Wesley Crusher and gives other advice, such as to stop pretending to be unintelligent. This is similar to a grooming process to allow another person to take over as leader, or in this case the dominant OS.
Wesley later warns Picard about Lore OS, but Picard scolds him and sends him off the bridge only to go back to the Lore OS. An uncharacteristically angry moment from the Captain, a sign that he also senses something, but is too embarrased or ashamed that he would feel that way about a trusted subordinate.

Throughout the episode, Data, not Lore is questioned as to how much he can be trusted. Captain Picard discusses it in the ready room with Riker and LaForge and then again Tasha Yar asks Picard the same question on the bridge. Why aren't they questioning if they can trust Lore, not Data? Data is an unemotional automaton that can't be disloyal. There's no reason for the questioning and certainly not by multiple crew members.
In the end scene battle, it shows Dr. Crusher hesitating to shoot Lore, a lifeless android, to protect her own son. This makes no sense unless she sees Data, not a separate android. The physical struggle is entirely between the two personas and ends up with the Lore OS in the transporter. A theatrical depiction of the android purging himself of the Lore OS or the evil within oneself.

Notice that after this is done, the body of Lore is not shown floating in space, nor is Captain Picard or anyone else interested in transporting him to the brig or even tractor beaming him to starfleet to reverse engineer, like they try to do later on in "The measure of a man" episode. This is too implausible to be believed. They know he can survive without oxygen or any other essentials, leaving him a security threat for enemy races to download all the information he aquired from the ship's computer.
What do they show? The crystalline entity retreating, but in reality it was delivering the Lore OS code to a compatible operating system. Where is the only place in the universe that has the compatibility to run the Lore OS? You guessed it, Dr. Noonien Soong’s residence, the next time we see Lore in the series.
Data does indeed have the information of Dr. Soong's location as he is recalled by a homing beacon type program in a later episode.
This only leaves one plot hole. If Lore isn't a seprate android, with his own nurtured experience leading up to evil, how did a Lore OS happen? It's because of the crystalline entity, whom is very, very evil.

The crystalline entity has the ability to transfer and receive information. It's able to transmit a message directly to Lore OS without any need for separate technology. When it found Data originally on the planet, it infected him wirelessly with a malicious virus that overrode his operating system, leading to Dr. Soong pulling out the neural net.

Thank you for reading. Please comment, upvote and stay tuned for part 2