The value of X is determined as Loot's last ability resolves.

You pay all costs and follow all normal timing rules for cards played from exile with Loot's last ability. For example, if the exiled card is a land card, you may play it only during your main phase while the stack is empty.

The card types that could appear among your nonland permanents are artifact, battle, creature, enchantment, kindred, and planeswalker.

Lands are disregarded when calculating the value of X. For example, if you control an artifact land but no other artifacts, artifact won't count toward the value of X.