After $C^{\infty}$-small Hamiltonian perturbation we may assume any intersection point $p$ between $L$ and $L^{\prime}$ is transverse. We can write the tangent planes of $L,L^{\prime}$ inside $T_{p}X\simeq\mathbb{C}^{n}$ in the standard form

$$T_{p}L=\mathbb{R}^{n}\subset\mathbb{C}^{n},\quad T_{p}L^{\prime}=(e^{i\phi_{1}},\ldots e^{i\phi_{n}})\mathbb{R}^{n}\subset\mathbb{C}^{n},\quad 0<\phi_{i}<\pi.$$

The Floer degree of the intersection point $p$ is

$$\mu_{L,L^{\prime}}(p)=\frac{1}{\pi}(\theta_{L}-\theta_{L^{\prime}}+\sum_{1}^{n}\phi_{i})>0,$$

whence $HF^{k}(L,L^{\prime})=0$ for $k\leq 0$. ∎