So-called flat-faced lifters, like the hydraulic lifters in your pushrod V6 engine, take a "set" when they contact the camshaft. For that reason, new hydraulic lifters would be a good idea with your new hydraulic camshaft, and help reduce the odds of wiping out your new cam via the "false economy" of reusing your engine's old hydraulic lifters.
Yes, I imagine
some people may have successfully pulled off reusing old hydraulic lifters, but that generally is not considered a recommended gamble. The recommendation to employ new hydraulic lifters with your new hydraulic cam isn't some clever conspiracy of the cam companies to sell you more parts; it's just a good idea, good insurance.