Is the grammar G left recursive?

Yes, because of the production E  $\longmapsto$  E $\bf ,$ S. Observe that from G we see that E is a sequence of S's seperated by commas, with at least one S. So we just need to swap E and S in the last rule to remove the left recursivity.

S	$\longmapsto$	$\bf a$
S	$\longmapsto$	L
L	$\longmapsto$	()
L	$\longmapsto$	(E)
E	$\longmapsto$	S
E	$\longmapsto$	S , E