Step 1: Understand the context of the question.
The question is about the role of Leg-haemoglobin in the root nodules of legumes. Root nodules are specialized structures formed on the roots of leguminous plants, which house nitrogen-fixing bacteria, primarily \textit{Rhizobium}. These bacteria perform biological nitrogen fixation, converting atmospheric nitrogen (\text{N}$_2$) into ammonia (\text{NH}$_3$), a form usable by plants.
Step 2: Recall the function of nitrogenase enzyme.
The enzyme responsible for nitrogen fixation is nitrogenase. A key characteristic of nitrogenase is that it is extremely sensitive to oxygen. Oxygen irreversibly inactivates the nitrogenase enzyme.
Step 3: Analyze the role of Leg-haemoglobin.
Leg-haemoglobin (legume hemoglobin) is a red-pigmented protein found in the cytoplasm of infected cells within the root nodules. It is structurally and functionally similar to animal hemoglobin. Its primary role in the nodule is to bind to oxygen with high affinity.
Step 4: Evaluate the given options based on the function of Leg-haemoglobin.
\begin{itemize}
\item (1) It transports oxygen to the root nodules. While leg-haemoglobin does bind oxygen, its role is not to \textit{transport} oxygen to the nodules for general metabolic purposes. Instead, it carefully regulates oxygen levels. High oxygen levels would harm nitrogenase. This option is incorrect.
\item (2) It protects nitrogen fixing enzyme from oxygen. This is the critical function. Leg-haemoglobin acts as an oxygen scavenger, maintaining a very low concentration of free oxygen within the nodule, thereby creating an anaerobic (or micro-aerobic) environment essential for the nitrogenase enzyme to function without being denatured by oxygen. This statement is True.
\item (3) It provides energy to the nitrogen-fixing bacterium. Energy for nitrogen fixation comes from the plant in the form of carbohydrates. Leg-haemoglobin is involved in oxygen regulation, not direct energy provision. This option is incorrect.
\item (4) It acts as a catalyst in transamination. Transamination is a biochemical reaction involving the transfer of an amino group, often catalyzed by enzymes called transaminases. Leg-haemoglobin is an oxygen-binding protein, not an enzyme involved in transamination. This option is incorrect.
\end{itemize}
Step 5: Conclude the correct option.
The most accurate role of Leg-haemoglobin in legume root nodules is to protect the oxygen-sensitive nitrogenase enzyme.
The final answer is $\boxed{\text{It protects nitrogen fixing enzyme from oxygen.}}$.