Thanks for your reply. In many papers, $g$ was always supposed to be self-dual. Maybe $g$ can be replaced by some symmetric square lift $\text{sym}^2g_1$ say, then for self-dual case, subconvexity bound boils down to evaluation of $L(\frac{1}{2},\text{sym}^2g_1 \times f)$. Is that right?? In many people's works(eg Blomer,M.P.Young, xiaoqing li), they do not use a symmetric square lift instead. The Kuznetsov formula on GL(3) works well, however I think maybe it's more effective form $GL(2)$'s point of view.