Lancashire boiler is a fire tube boiler.

Explanation:
A fire tube boiler is a type of boiler in which hot gases pass through the tubes and water surrounds these tubes for heat transfer. The Lancashire boiler is a type of fire tube boiler.

Here is a detailed explanation of each option:

a) Lancashire boiler is a fire tube boiler:
- The Lancashire boiler is a horizontal, internally fired, and natural circulation type of fire tube boiler.
- It consists of two large cylindrical shells, called furnace shell and boiler shell, that are connected by a number of tubes.
- The furnace is located inside the furnace shell, where the combustion of fuel takes place.
- The hot gases produced by the combustion pass through the tubes and exchange heat with the surrounding water.
- The water is present in the boiler shell, which surrounds the tubes.
- This heat transfer process generates steam that is collected in the steam space of the boiler shell.

b) Fire tube boilers are internally fired only:
- Fire tube boilers can be either internally fired or externally fired.
- In internally fired boilers, the furnace is located inside the boiler shell, as in the case of the Lancashire boiler.
- In externally fired boilers, the furnace is located outside the boiler shell, and the hot gases are directed through the tubes.

c) Babcock and Wilcox boiler is not a water tube boiler:
- Babcock and Wilcox boiler is a type of water tube boiler.
- It consists of a number of parallel tubes, through which water flows.
- The tubes are connected to a steam drum and a mud drum, forming a continuous circuit for water and steam circulation.
- The hot gases pass over the outside of the tubes, transferring heat to the water inside.
- This type of boiler is commonly used in power plants.

Therefore, the correct statement is option 'a' - Lancashire boiler is a fire tube boiler.