This is definitely false with requiring ample.
Let $M=M_1\times M_2$ and $D_i$ the pull back of an anti-canonical divisor on $M_i$. Then $D_1+D_2\in |-K_M|$ but they are individually not ample. (They are nef though).
I don't know what you $\lambda$ is, but if you want coefficients strictly between $0$ and $1$, then choose two different anti-canonical divisor on each factor and multiply them by $1/2$.