The Labor Theory of Value has been replaced by the theory of Marginal Utility, which was already accepted by Marx time. In fact he acknowledged:
"nothing can have value, without being an object of utility"
-Wikipedia: Marginal Utility - The Marginal Revolution and Marxism
Marginal Utility addresses the diamond - water paradox by explaining that the more of a resource or commodity one has ready access to, the less one needs access to even more. The declining marginal utility means that because water is nearly ubiquitous and easily accessed it has very little "value" per unit to an individual because they know they have access to many many units.
"Modern" analytical Marxists, including John Roemer have built a strong foundation (if somewhat heterodox) based on the theory of marginal utility.