I don't know how detailed your little debate is but if the conversation is about modern Marxist economics then I recommend Michael Roberts Marx 200.

It is very easy to prove the LTV in a modern context. Marx predicted profitability would fall and this would cause recurring crises where the only course of action would be neoliberalism. Michael does a very good job presenting evidence for this.

I would not bother debating LTV in an abstract context because neoliberalism(I assume this is your opponent) thrives on conceptual nonsensical unproven unscientific "theories" and assumptions, the whole free-market shit is ideology, not empirical science.

Bring the conversation down to empirical science with actual real world economic data e.g neoliberalism of the 80s coincides with the first crisis and the end of the "golden era" of capitalist profitability.