Step 1: Understanding the Concept:
Lucerne (also known as Alfalfa) is a premier perennial leguminous forage crop termed the 'Queen of Forages'.
Step 2: Detailed Explanation:
The official botanical taxonomic name of Lucerne is Medicago sativa L., belonging to the family Fabaceae (Leguminosae).
It is valued for its high crude protein content ($18\text{--}22\%$) and perennial productivity under irrigated conditions.
Step 3: Final Answer:
Therefore, the botanical name of Lucerne is Medicago sativa.