If an effect (such as the one from Lodestone Golem) imposes an additional generic mana cost to casting Khalni Hydra, the Hydra's ability will reduce it too. It'll reduce the amount of green mana you need to spend first, though.

For the purpose of determining the cost reduction, the number of green creatures you control is checked as you cast Khalni Hydra, before your last chance to activate mana abilities to pay for it. For example, if you control Wild Cantor (a red and green creature with the ability "Sacrifice Wild Cantor: Add one mana of any color.") as you cast Khalni Hydra, first the cost to cast Khalni Hydra is reduced by {G}, then you could sacrifice Wild Cantor for mana to help pay for it.

Khalni Hydra's cost reduction effect doesn't change its mana cost or mana value.