Do we have $e(G)=l(G)$ always for any first countable paratopological group.?

Question

Let $G$ be a (Hausdorff, regular, Tychonoff) first countable paratopological group.

Do we have $e(G)=l(G)$ always? (Clearly, $e(G) \le l(G)$.)

Definitions:

1. The Lindelof number $l(X)$ of a topological space $X$ is the smallest number $\kappa$ such that every open cover of $X$ has a subcover the cardinality of which is at most $\kappa$.

2. The extent $e(X)$ of $X$ is the supremum of the cardinalities of closed discrete subsets of $X$.

Thanks for your help.