I don't see what it is you believe relies on the labor theory of value.
Marx theories span a wide range, but certainly his political ideology did not in any way rely on the labor theory of value to underpin it, and it is something most people advocating Marxism don't even know or understand very well.
What it does rely on is whether Marx hypothesis that capitalism will necessarily self destruct as it reaches the limits of market expansion is correct (no more people living out of reach of capitalist competition). Marx expected this to happen by forcing capitalists into ever harsher competition and automation at the cost of starting to throw workers back into poverty and as a result pulling the rug out under their own markets, eventually leading to sufficient social upheaval to drive the working classes to revolution.
It further relies on Marx hypothesis that upon the self destruction of capitalism, that the working classes can end the class struggle by seizing control and redistributing wealth and the control of the means of production.
The LTV is used by Marx as justification for why some of this is "right", but at the same time Marx theories on the political and economic development of society does not rest on right and wrong, but on how the self-interests of the members of the various classes affects society as the economic development alters the relative powers of these classes.
There are plenty things that can be wrong in these theories, but whether or not the LTV is right or not is an entirely orthogonal issue.