Why didn't the doctor tell K the truth

She could have at least said it looked like an implant.

Because selling real memories to the Wallace Corporation is illegal for her to do, and considering that she has a compromised immune system and would likely get sick if she stepped out of her glass room, I’m sure she wasn’t prepared to admit what she had done and likely go to prison for it.

She was adding her own memories to replicants in order for them to find her father and bring him to her. If she told K it was an implant (no matter from whom), he did not have any reason to follow these memories, which were leading to Deckard. He would however have a reason to investigate (after all he is with the cops) who illegally implanted these memories.
Also Wallaces Replicants obey their owner, so she couldn't trust him with the truth directly. He had to figure it out alone. Although she didn't know it: Don't forget that Wallace was still somehow monitoring K, since Luv was able to find him in Vegas.