To solve this logical reasoning problem, we need to determine the seating arrangement of six students: Sarah, Tom, Lily, John, Mike, and Emma, who are sitting in a circle facing the center. Let's analyze the given conditions step-by-step.

1. Firstly, the statement "John is sitting third to the left of Lily and is between Sarah and Tom" gives us the position of John relative to Lily. This implies that Lily is two positions to the right of John, and John is exactly between Sarah and Tom.
2. The condition "Sarah sits to the immediate left of Mike" allows us to position Sarah and Mike relative to each other. Therefore, Mike is to the immediate right of Sarah.
3. We are also informed that "Tom is not a neighbour to Mike." This information can help eliminate any incorrect arrangements.
4. Based on the conditions, start by placing John between Sarah and Tom. Since John is third to the left of Lily, place Lily accordingly. This helps define the initial structure.
5. Knowing Sarah is to Mike's immediate left, place Mike. Ensure Tom is not adjacent to Mike, following the third condition.
6. With only one person left, it must be Emma, placed in the remaining position. Since the circle has only one free spot at the end, this fills the entire arrangement.

Let's finalize the arrangement:

- Arrange John with Sarah and Tom on either side, which places Lily in the correct position two spots to the right of John.

- Position Sarah to Mike's left, ensuring Tom is not beside Mike.

- Finally, place Emma, completing the circle.

Based on this seating arrangement, the person sitting to the immediate right of Emma is Tom.

Thus, the correct answer is Tom.