精益 is not really one word. It is actually a combination of:
精, meaning "pureness"
益, meaning "benefit", i.e. profit.
Combining the two gives us something like "purely beneficial (to the bottom line)". This is similar enough to the "lean manufacturing"'s idea of "no unnecessary frills" to serve as a translation.
精益生产 is an established (more or less) translation for "lean manufacturing", 精益 can be considered a noun and an abbreviation. But the above breakfown is where the root of the translation comes from.
This is different from the phrase
精 means "good" or "high quality" and
益 is an adverb meaning "further more". That is, "already high quality but seeking further improvements".