Also:

    ClearAll[toLTM]
    toLTM[n_Integer] := Composition[Transpose, PadLeft, Range, Reverse, Range]@n
    (* or toLTM[n_Integer] := Reverse /@ PadLeft @ Range @ Range @ n *)

    toLTM[v_List] := Reverse /@ PadLeft @ Extract[v, List /@ Range @ Range @ Length @ v]

    toLTM @ 4 // TeXForm
> $\left(
\begin{array}{cccc}
 1 & 0 & 0 & 0 \\
 2 & 1 & 0 & 0 \\
 3 & 2 & 1 & 0 \\
 4 & 3 & 2 & 1 \\
\end{array}
\right)$

    toLTM @ CharacterRange["a", "d"] // TeXForm
> $\left(
\begin{array}{cccc}
 \text{a} & 0 & 0 & 0 \\
 \text{b} & \text{a} & 0 & 0 \\
 \text{c} & \text{b} & \text{a} & 0 \\
 \text{d} & \text{c} & \text{b} & \text{a} \\
\end{array}
\right)$