#lagrange and $LALa girlfriend in English translates to girlfriend in English. It can also be used informally to mean friend. The definite article the indicates that it's a specific girlfriend or friend, not just any one.
Here's a breakdown:
The:
This is the English definite article for feminine singular nouns. It's like saying the in English.
Girlfriend:
This word means girlfriend or, more generally, friend (when referring to a female).
Therefore, the girlfriend refers to a specific girlfriend or female friend.