In-universe, maybe <PERSON> made up a name for him without realizing its normal use.
Calling Lord <PERSON> <PERSON> is the Death Eaters' term of respect for him. It's not something said by people who oppose him. However, <PERSON> would most likely not know that. She is young, and would not know much about him or the Death Eaters.
In her love poem, she is saying a lot of things that she likely made up herself. She's comparing <PERSON>'s eyes to toads and his hair to a blackboard, and I doubt that even in the wizarding world, those are common idioms or that she's heard anyone else using those analogies.
So it's possible she made up her own way of referring to Lord <PERSON>, and it's just a coincidence that it happened to be the name that the Death Eaters call him by. She wouldn't have thought twice about using the term she made up, because she wouldn't realize its usual significance.
(Although he wasn't lovestruck and writing a poem at the time, this may be the case for why <PERSON> called Lord <PERSON> the Dark Lord as well.)
Out-of-universe, it could be a continuity error.
When commenting on the question, <PERSON> pointed out something interesting. 247
Also in Harry Potter and the Chamber of Secrets, <PERSON> called Lord <PERSON> the Dark Lord as well.
(<PERSON> calling him <PERSON> makes sense. Up until <PERSON> freed him, he was the house elf to the <PERSON>. <PERSON> was a Death Eater, so he would call Lord <PERSON> the Dark Lord, and so would all the other people frequently around him. <PERSON> would have learned the term from them, and called Lord <PERSON> the only name he knew for him, despite his opinions on the Dark Lord being different from the <PERSON>'.)
My theory is that when this book was written, <PERSON> hadn't yet decided that she wanted the Death Eaters to call him <PERSON>, and was just using it as a general term. Later, when both Lord <PERSON> and the Death Eaters were a bigger part of the story, she decided to make "<PERSON>" be the term of respect that the Death Eaters used for their master.
I'm fairly sure that after the Death Eaters become a large part of the story, they and the people around them or controlled by them are the only ones to call him <PERSON>. <PERSON> doesn't count, because he was pretending to be one, so would have to use the same name they would. 247