I have read some Plato, but not the parts relevant to my question (alas). I do know that artistic making is meant to be a copy of a copy (the world) of platonic forms. But how does that fit in with lyric poetry, which seems to me to be an expression of ourselves rather than a copy of a shadow? Are the personal thoughts and feelings that are expressed in lyric poetry imitations of things in the world? Or are lyrics expressions of the knowledge about forms we have remembered? If neither of these, then what is the lyric self?
Plato claims that
Poetic narration can take place through narration alone, through mimêsis alone, or with a mix of the two (392d).
So poetry can, but need not be, purely imitative. Poets themselves have no (philosophical) knowledge, but poetry can also be inspired (by the gods).
It may be worth noting that
ancient ideas of mimesis often encompass a dimension of what would now be counted, by many aestheticians, as expression, and that representation and expression are not mutually exclusive concepts in the interpretation of art
The quarrel with poetry includes lyric poetry, and poetry is
little more than the poet’s unargued imaginative projections whose tenability is established by their ability to command the applause of the audience. That is, the poets are rhetoricians who are, as it were, selling their products to as large a market as possible, in the hope of gaining repute and influence.
I am unsure how exactly Plato accounts for the internal life of poets, beyond how ignorant they are, but I would guess that an account of 'lyric' in his terms would involve the interface of 'expression' and 'narration'.
For Plato, the material world that we live in is just a degraded copy of a more perfect, more abstract world. The things of that other world can be imitated but never perfectly, described, but never perfectly. The only way to truly apprehend them is by direct intuition, which Plato conceptualized as your eternal soul remembering the things that it experienced before it entered the material world.
Anything for Plato is good and desirable to the exact extent that it moves people towards the more true and eternal world, and bad and to be avoided to the extent it moves people away from it. Accordingly, artists, poets, and storytellers are very ambivalent figures in Plato's work. They potentially can move people either direction. One poem could awaken the listener to the existence of True Beauty, but a superficially similar one could ensnare the listener in a deceptive illusion. One story is an allegory for the higher world, the other is just a meaningless fable.
In the case you've mentioned, it would depend on what the poet was depicting. In the Ion, Plato claims that all good art comes by "divine inspiration" which is just another way of him saying we have to move our egos out of the way and let our eternal souls remember the Real World. A poem inspired that way elevates the listener. If, however, the poet is talking about their own feelings and experiences of the material world, that would be bad art in Plato's book. It would tie us more to materialism, and thus move us away from the Eternal.