Let $W_t$ be a Brownian motion under probability measure $\mathbb{P}$. Let $X_t$ be defined as follows.
$$\mathrm{d}X_t = a \mathrm{d}t + 2\sqrt{ X_t} \mathrm{d}W_t.$$
Also define: $$L_t = \exp\left(-\frac{k}{2}\int_0^t \sqrt{X_s}\mathrm{d}W_s-\frac{k^2}{8}\int_0^t X_s\mathrm{d}W_s\right).$$
How to show $L_t$ is a martingale? Is there a Leibnitz rule for Ito's lemma which can help write $\mathrm{d}L_t$?