Can I Tideturner a unit out of Vilemaw Lair?

No, you cannot use Tideturner to move a unit out of Vilemaw's Lair.

According to the RiftJudge FAQ (ID 7241) regarding this specific interaction:

• Ruling: You cannot move a unit out of Vilemaw's Lair using Tideturner's swap ability. Because Tideturner's effect uses the word "move," it is subject to the restriction of Vilemaw's Lair, which prevents units from moving from it to your base.

Sequence of the interaction:

1. Tideturner is played to your base and targets the unit in Vilemaw's Lair.
2. Tideturner moves to Vilemaw's Lair.
3. The targeted unit cannot move to your base due to the restriction imposed by Vilemaw's Lair.
4. The targeted unit remains in Vilemaw's Lair.

Nuances:

• The swap effect still partially resolves: Tideturner successfully moves to Vilemaw's Lair, even though the other unit is prevented from moving out.
• Vilemaw's Lair prevents all movement effects to base, not just standard moves. Only "Recall" effects (which are distinct from movement) can bypass this restriction.