If Pyrogoyf or the relevant Lhurgoyf creature leaves the battlefield while Pyrogoyf's last ability is on the stack, use its power as it last existed on the battlefield to determine how much damage is dealt.

Card types that can appear on cards in a graveyard are artifact, battle, creature, enchantment, instant, kindred, land, planeswalker, and sorcery. Legendary, basic, and snow are supertypes, not card types; Lhurgoyf, Forest, and Siege are subtypes, not card types.

The ability that defines Pyrogoyf's power and toughness counts card types, not cards. If the only card in all graveyards is a single artifact creature card, Pyrogoyf will be a 2/3. If the cards in all graveyards are ten artifact cards and ten creature cards, Pyrogoyf will still be a 2/3.

The ability that defines Pyrogoyf's power and toughness works in all zones, not just the battlefield.