3 of 3 added 19 characters in body

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] := Transpose @ 
  PadLeft @ Extract[v, List /@ Range @ Reverse @ 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

$\left( \begin{array}{cccc} \text{a} & 0 & 0 & 0 \\ \text{b} & \text{a} & 0 & 0 \\ \text{c} & \text{b} & \text{a} & 0 \\ \text{d} & \text{c} & \text{b} & \text{a} \\ \end{array} \right)$