A lot of it has to do with concordance. One big example—one that has theological significance—is the Hebrew word זֶרַע (seed). The NASB translates it sometimes as "seed," other times as "offspring," and still more times as "descendant(s)." The NASB 2020 is even worse (see Genesis 3:15 for an egregious example). The LSB chose to make their translation very concordant for this word and others, which helps the reader see the biblical-theological significance of the word. The ESV does this, too, but uses "offspring," since it too is an English word which can take the singular and plural without changing form. The CSB uses "offspring," as well, which is a major upgrade from the HCSB. (By the way, I know concordance can be taken too far; not every word needs to be translated the same way all the time. However, there are some instances where it really should, and זֶרַע, in my opinion, is one of them.)Now I am curious, what inconsistencies are you talking about?
Another thing the LSB has fixed is just weird translation inconsistencies in the NASB that just made no sense. An example that I can think of is 1 Peter 1:2 and 2 Peter 1:2. Look at the difference (this maintains for the NASB77, as well):
"Grace and peace be yours in the fullest measure" (1 Peter 1:2).
"Grace and peace be multiplied to you" (2 Peter 1:2).
The Greek in both cases is the exact same: χάρις ὑμῖν καὶ εἰρήνη πληθυνθείη. The NASB even has a footnote for 1 Peter 1:2—"Lit be multiplied for you." So why in the world not just put the "literal" rendering in, like 2 Peter 1:2 (though, oddly, even the "literal" footnote is different than 2 Peter 1:2, using "for" instead of "to")? I cannot for the life of me figure it out. I know the meaning is virtually the same, but it makes me wonder where else this kind of thing occurs in the NASB.
The LSB, thankfully, fixed this and likely many other weird issues with the NASB.