I suppose the terminology of height of a node may be confusing here, so let's make it clear first how I interpret it:
The height of the root is 0; if a node has height $j$, its children has height $j+1$. Being above means having larger height, i.e. further from the root. Thus, one thinks of the root at the bottom and the leaves at the top, not the other way around.
If the tree has $m_j$ leaves at height $j$, where $h$ is the maximal height (i.e. $\sum_j$ means $\sum_{j=0}^h$), then $l=\sum_j m_j$ and $l\cdot t=\sum_j jm_j$. Let me rephrase the problem slightly: for any $a>0$ (where $a=kt$ in the original), there are at most $lt/a$ leaves with height $j\ge a$. This follows from $\sum_{j\ge a} m_h =\frac{1}{a}\sum_{j\ge a} am_j \le\frac{1}{a}\sum_{j=0}^h jm_j =\frac{lt}{a}. $
The requirement that $k\ge1$ (i.e. $a\ge t$) is not required, only that $a>0$. Of course, the only interesting values of $a$ are integers.
It may also be noted that the result doesn't make use of the fact these are leaves on a binary tree: they are just leaves with values (in this case height) attached to them.