I think He is saying that statement of option $(B)$ is false and hence is the answer too.

$(A)$ given lattice is distributive but it is not a complemented lattice. Because complemented lattice must be bounded and each element must have at least one complement.So, → $True$

$(B)$ this is not a lattice. $\rightarrow False$

$(C)$ This is not a boolean lattice. $\rightarrow True$

because, In boolean lattice every element has complement. This is not true in given lattice.

$(D)$ $1$ has not a complement. It’s true infact in our lattice no element is having a complement. So $\rightarrow True$

So false statement is $(B)$ and hence answer.