Noncontext free for quotient
Work backwards, from right to left.
Try to find which strings of the form $a^*$ belong to $L_1/L_2$. So find matches of strings $w_1\in L_1$ and $w_2\in L_2$ such that at the start only a string of the form $a^*$ sticks out: $w_1= a^k w_2$.