Certainly it can explain it. The bespoke handbag has the labor of manufacturing done in one place, the machine-manufactured handbag has the labor of manufacturing done in two places - the place of manufacture and the place where the machine was manufactured.
The "Marxist" labor theory of value was held by Benjamin Franklin, Adam Smith and all of the pre-Marxist political economists I know of. It is also a theory you seem to know little about as you're constructing a false, strawman notion of what LTV is and then knocking it down. Not that you're alone in this, I've read Paul Krugman attribute theories to the LTV which its proponents never had, so as to, like you, knock down the strawman theories. I honestly believe he is doing it out of ignorance as opposed to malice.
Actually, like all economic theories, the LTV does have holes which serious critics have pointed out. You don't seem to know what those are though.