  We study $\mathbb{Z}_2$-graded identities of Lie superalgebras of the type
$b(t), t\ge 2$, over a field of characteristic zero. Our main result is that
the $n$-th codimension is strictly less than $(\dim b(t))^n$ asymptotically. As
a consequence we obtain an upper bound for ordinary (non-graded) PI-exponent
for each simple Lie superalgebra $b(t), t\ge 3$.
