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I want to describe a girl's yearning for a guy who'll never love her back. The sentence is "her skin was unsheathed to lure her lover's eyes". I want to remove the ambiguity in this sentence by replacing the word "lover," since that could imply that he loves her back.

There are some one-word possibilities, none perfect.

"her skin was unsheathed to lure her unrequited's eyes"

Unrequited by itself is pretty unambiguous, given that it is almost always used in conjunction with "love", but this isn't – strictly speaking – particularly grammatical.

"her skin was unsheathed to lure her beloved's eyes"

Beloved fits grammatically, but like flame in Wordster's answer, it doesn't rule out that the feeling may be reciprocated. The same goes for "her desired's", although that word implies reciprocation a bit less strongly (desire/desired carries a sense that the object has not – at least yet – been obtained), but is somewhat awkward to say.

"her skin was unsheathed to lure her idol's eyes"

Idol is pretty good in terms of non-reciprocation, but makes the person into an object of veneration, not merely love.

"her skin was unsheathed to lure her infatuation's eyes"

Infatuation is even closer but still – somewhat like idol – may imply a certain sense of obsession that mightn't be what you're looking for (and somewhat obviously this goes double or more for "her obsession's").

"her skin was unsheathed to lure her inamorato's eyes"

Inamorato is almost perfect (only establishes a one-way loving relationship, with no reciprocation implied), but is a really uncommon loan-word (from Italian, as it happens), and will make most readers pause to understand – or even look up – the word.

"her skin was unsheathed to lure her crush's eyes"

Crush – I think – is the best option for this context, since (although it technically suffers from the same flaw as flame, beloved, desired, etc.) it is usually used in the sense that the object doesn't reciprocate the feeling (or may even be unaware of it).

The one weakness with crush is that it doesn't specifically imply an emotion as strong as mature love, but could be a more juvenile feeling, like what is usually called puppy-love.

Flame

object of one's passionate love

"her skin was unsheathed to lure the eyes of the object of her limerence"

limerence in British English (ˈlɪmɪrəns) noun

psychology:

A state of mind resulting from romantic attraction,

characterized by feelings of euphoria,

the desire to have one's feelings reciprocated, etc.

The term came about in the late 70's:

Limerence, a term coined by psychologist Dorothy Tennov in her 1979
book Love and Limerence: The Experience of Being in Love

With the desire for, but without the necessity for any reciprocation for it to happen, it's explained:

Much to the dismay of diehard romantics, research suggests that
limerence is the result of biochemical processes in the brain.
Responding to cues from the hypothalamus, the pituitary gland releases
norepinephrine, dopamine, phenylethylamine (a natural amphetamine),
estrogen and testosterone. This chemical cocktail produces the
euphoria of new love and begins to normalize as the attachment
hormones (vasopressin and oxytocin) kick in.