The Lair is a spawnpoint card and Spawnpoints cast creatures themselves. During your Planning phase you select the appropriate creature card and attach it faced own on the spawnpoint. During the Deployment phase the spawnpoint casts the attached creature card assuming the spawnpoint's conditions are met (usually the spawnpoint must have a minimum amount of mana on it before it can summon).
The spawnpoints have a channel value, and as such generate their own mana pool which is separate from the Mage. In the case of your Lair, that is 2 mana per turn. If you have enough mana on the spawnpoint to deploy the creature but not enough to pay for the attached creature spell's total mana cost, you pay the remaining amount from the Mage's mana pool. Note the spawnpoint is still the caster of the spell been when the Mage pool is used.
You may enchant a spawnpoint with with appropriate spells, namely Harmonize. This would give your lair a channel of 3 which really opens the animal floodgates for the Beastmaster!
I hope this post helped but feel free to ask a followup if you need. This forum has a great community and someone will help you, usually very quickly.