Does Hellkite Tyrant in combination with Mycosynth Lattice steal lands?
Yes, as you stated correctly, lands are permanents:

110.1. A permanent is a card or token on the battlefield.
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110.4. There are five permanent types: artifact, creature, enchantment, land, and planeswalker.

Enemy Lands are Artifact [Basic] Lands now due to Mycosynth Lattice, and nothing stops you from getting control of them if you deal combat damage with Hellkite Tyrant.