Combine the eggs, vanilla extract, lime juice, melted butter, melted coconut oil, XCT oil, and erythritol in a high-speed blender.
Secure the lid and blend on high speed for 30-60 seconds, or until the mixture is completely smooth, creamy, and emulsified.
With the blender running on low, slowly stream in the water.
Add just enough to achieve a thick but pourable consistency, similar to a heavy cream or a thin milkshake. You may not need the full cup.
Pour the ice cream base directly into the frozen bowl of your ice cream maker.
Churn according to the manufacturer's , typically for 20-25 minutes, or until it reaches a thick, soft-serve consistency.
Serve immediately for a soft-serve style treat, or transfer to a freezer-safe container and freeze for at least 2-3 hours for a firmer, scoopable ice cream.
Let the frozen ice cream sit on the counter for 5-10 minutes before scooping to allow it to soften slightly for easier serving.