It will give you the complete song lyrics which are under copyright.
The infringement occurs at the time of copy, not at the time of training.
What you can't do is distribute the lyrics without the author's permission.
When you ask DeepSeek to retrieve the lyrics (and it does so), the real question is this: Is DeepSeek merely acting as an intermediary/ISP according to the DMCA (in which case they'd be protected under the safe harbor clauses) or are they illegally redistributing the lyrics without the author's permission?
Whether or not you own a copy of the lyrics is irrelevant from a legal perspective in this scenario.
My guess: If they just retrieved the lyrics from some website and delivered them to you (because you asked), they're an ISP. However, if they pulled them out of their own database, they're violating copyright.
LLMs are far too lossy to be able to store such lyrics in their entirety. In fact, they're not even "lossy" since they're not even trying to record such information. They're just weights for how likely it is that any given word will come after another.