Lozenge tilings

You can add the options ViewProjection, ViewPoint, and ViewVertical to make it appear as if it isometric:

coversQ[parent_,child_]:=And[Length[parent]>=Length[child],Min[Take[parent,Length@child]-child]>=0]

planepartitionQ[par_]:=MatchQ[par,{{___Integer}..}]&&If[Length[par]>1,And@@MapThread[coversQ,{Drop[par,-1],Rest[par]}],True]

PlanePartitions[n_Integer]:=Module[{l1,l2,l3,l4,z,w},l1=z@@@IntegerPartitions[n];
l2=l1/.k_Integer/;(k>1):>w@@IntegerPartitions[k];
l3=l2/.z[x_w,y:(1...)]:>Thread[z[x,y],w]/.z[x__w]:>Outer[z,x]/.z[x__w,y:(1...)]:>Outer[z,x,Sequence@@({y}/.1->w[1])]/.w->Sequence;
l4=l3/.z[x___List,y:(1..)]:>z[x,Sequence@@Transpose[{{y}}]]/.z->List;Cases[Union[l4],_?planepartitionQ]]
PlanePartitionDiagram[l_List]:=Module[{i,j,k},
Graphics3D[{EdgeForm[{Black,Thickness[0.01]}],
Table[
Cuboid[{j,-i,k}]
,
{i,Length[l]},
{j,Length[l[[i]]]},
{k,l[[i,j]]}
]},
Boxed->False,
ViewProjection->"Orthographic",
ViewPoint->{1,1,1},
Lighting -> {{"Directional", 
   Yellow, {{0, 0, 1}, {0, 0, 0}}}, {"Directional", 
   Blue, {{0, 1, 0}, {0, 0, 0}}}, {"Directional", 
   Red, {{1, 0, 0}, {0, 0, 0}}}}
]
]
PlanePartitionDiagram[{{3,3,2,1},{0,3,2,1},{0,3,2,1},{0,0,0,1}}]

(should work with 11.2 and up).

Here is different way to achieve the coloring:

PlanePartitionDiagram[l_List, col_, {offsetx_, offsety_, offsetz_}] :=
  Module[{i, j, k},
  Graphics3D[
   Prepend[Glow[col]]@Table[
     Cuboid[{j + offsetx, -i + offsety, k + offsetz}],
     {i, Length[l]},
     {j, Length[l[[i]]]},
     {k, l[[i, j]]}
     ]
   ]
  ]

Show[
 PlanePartitionDiagram[{{3, 3, 2, 1}, {0, 3, 2, 1}, {0, 3, 2, 1}, {0, 0, 0, 1}}, Red, {10^-2, 0, 0}],
 PlanePartitionDiagram[{{3, 3, 2, 1}, {0, 3, 2, 1}, {0, 3, 2, 1}, {0, 0, 0, 1}}, Blue, {0, 10^-2, 0}],
 PlanePartitionDiagram[{{3, 3, 2, 1}, {0, 3, 2, 1}, {0, 3, 2, 1}, {0, 0, 0, 1}}, Yellow, {0, 0, 10^-2}],
 Lighting -> None,
 Boxed -> False,
 ViewProjection -> "Orthographic"
 ]