The philosophy of the Labor Theory of Value is irrelevant to determining whether or not it's actually true: we must depend on empirical tests. However, the philosophical justification is important to understanding what the Labor Theory of Value actually says, and how it can be empirically tested.
The LTV starts with the observation that how human beings use our physical bodies over time is the only sort of decision or choice we can directly make; every other kind of choice (at least choices that have physical effects) results from our choice as to how to employ our labor. Since labor is the only thing we physically can make direct choices about, it seems at least plausible to hypothesize that the amount of labor will determine prices.
The LTV assumes that all labor has equal "intrinsic" value. There are more or less valuable ways that someone can use her labor, and there are particular characteristics of individuals that allow them to employ their labor more effectively for some uses and less effectively for others. The point of the "equal value" premise is to say that an hour of Jane Doe's labor is not more valuable just because she happens to be Jane Doe — or more realistically, just because she's white or her parents were royalty, nobility or of a particular economic class. It does not contradict the LTV to say that because Jane Doe is smart, hard working, talented, charming, and sociable, she therefore can put her labor to more valuable uses than could the dull, lazy, obnoxious John Smith. It would contradict the LTV to say that because Jane Doe is smart, etc. her labor is intrinsically more valuable than John Smith's regardless of the uses to which they put their labor.
Note too that the LTV, by incorporating the notion of abstract labor time, does not make any assumption at all about the variability of individual characteristics that allow people to put their labor to more or less valuable uses. The abstract qualifier is empirically meaningful to the extent that we can independently measure these individual characteristics and correlate them both empirically and theoretically to different uses of labor. For example, we can to some degree independently measure "intelligence" and correlate these measurements both empirically and theoretically to labor of more or less value. ("intelligence" tests measure only very narrow and specific cognitive abilities, and the relatively small differences between ordinary human beings in what "intelligence" tests measure does not come close to explaining actual differences in pay. Bill Gates might be smarter than me, but it seems unlikely he's even a thousand times smarter than me.)
Note that the "Libertarian" theory that all differences in pay are necessarily or by definition due to different individual characteristics that afford higher-paid people the ability to put their labor to more valuable uses is an entirely different (vacuous and unscientific) theory, lacking the critical components of independent measurement and theoretical justification. A CEO making $10,000,000 per year has mystery qualities compared to a top research scientist making $100,000 per year: We "know" the CEO must have better qualities because he is paid more; we don't know he is paid more because he has different measurable qualities.
The rest of the LTV follows directly from the ordinary assumptions of the ideal free market of independent, self-interested, rational individuals making mutually beneficial choices. Of course, the ideal free market is itself an ideal theory: it makes a number of assumptions that don't actually obtain in the real world.
It bears repeating: The Labor Theory of Value (as well as the ideal free market) is not intended to be a complete explanatory theory. It is, rather, half of a reduced theory: Just as Newton reduced celestial and terrestrial motion to inertia plus gravity, the LTV reduces economic behavior to labor plus externalities. The empirical value of the LTV thus depends on being able to independently measure externalities, correlate externalities to economic behavior, and empirically demonstrate that without the externalities, prices would correspond directly to labor time.
