I eat lemons like I eat oranges

[jeffalot]

For me, your poem discusses self-harm; with that in mind, my reply is given in the spirit of this forum.

I eat lemons like I eat oranges, - I've added a longer note below about this line.
I dig a nail into a lemon  - dig/nail - good, visceral imagery
peel its skin off peel away might actually works better here and could match with your next line...what about "peel away its waxy skin"
Picking off strings of pulp. "pick off its strings of pulp"

I peel it like an orange,
finger through the center peeling off individual slices  too much repetition of peel: once from the last stanza and twice in this stanza: I peel it... peeling off.
 line them out on a ceramic plate ok, good image, but give me a sense of your thoughts or mood here: are the segments neat or messy; what are your thoughts? 

I eat lemons like I eat oranges
I survive carelessly like I live with insecurity  you've abandoned your metaphor/simile and you're suddenly telling instead of showing / 'painting a picture'.
I take all good with a grain of salt, I digest deleterious materials  deleterious is a great word but this line is too long and doesn't make sense within your poem's own logic

I eat the slices off the plate sugar-coated
They burn and sting the roof of my mouth you're harming yourself physically
but it feels so good                                 
a vile taste  vile seems too obvious, needs something more descriptive, how does it feel, what is the sensation or the reaction of your body 
head-clearing excellent
fresh and fruitful layered imagery, multiple meanings - great!

I eat lemons like I eat oranges
I slice into my skin like pulp,  this is very visceral imagery. But again, you have abandoned your metaphor and now are directly writing of your own skin.
Bloody, thick juices flowing out You could be more subtle by perhaps considering a blood orange - the reader would understand, but you would be working within your original imagery.

I love the things I hate   this stanza is unnecessary. The statements are bland and do not fit with your theme. 
I cry like I smile
I run away like I sleep
I hurt myself like I know what’s best for me

I eat lemons like I eat oranges,
I peel off slices,
put them in a lunchbox
A side with a sandwich
Just as much vitamin C as an orange A jarring phrase, both in terms of rhythm and register.
the same shape,  
But yellow, agonizingly bitter
Faster erosion of enamel. the idea is good, but has an awkward formulation.

I eat lemons like I eat oranges.
Even though I don’t like lemons.   this last line is weak in terms of meaning (you already said lemons taste vile, and no one eats lemons on their own for the taste) and in terms of form its a weak sound/word to end on. 

"I eat lemons like I eat oranges” is strong in its simplicity, but it feels a little off-kilter rhythmically (which may be intentional). The line has internal repetition (eat...eat) and repeats throughout the poem. It creates a mantra-like effect, but there is no variation or development in meaning.

You might consider a more stylized alternative, like: “I eat lemons - as though, an orange.” This keeps the sense of comparison, and gives a deliberate pause. The construction allows for enjambment to extend the thought in the next line.

I hope you find my comments useful.