Lighting a ListPlot3D with a Texture

Question

I want to apply Lighting to some ListPlot3Ds with Texture applied, but it's not taking as it does with Plot3D. As an example,

p[x_, y_] := PDF[MultinormalDistribution[{25, 25}, {{25, -12.5}, {-12.5, 25}}], {x, y}];

(* too dark *)
Plot3D[p[x, y], {x, 0, 50}, {y, 0, 50}, PlotPoints -> 50, 
 PlotStyle -> Blend[{Blue, Red}, 0.5], ViewPoint -> {-1.8, -2.2, 1}, 
 AxesEdge -> {{-1, -1}, {-1, -1}, {-1, 1}}, PlotRange -> {0, All}, 
 MeshFunctions -> (Sqrt[#3] &), Mesh -> 50]

(* better with Lighting *)
Plot3D[p[x, y], {x, 0, 50}, {y, 0, 50}, PlotPoints -> 50, 
 PlotStyle -> Blend[{Blue, Red}, 0.5], ViewPoint -> {-1.8, -2.2, 1}, 
 AxesEdge -> {{-1, -1}, {-1, -1}, {-1, 1}}, PlotRange -> {0, All}, 
 MeshFunctions -> (Sqrt[#3] &), Mesh -> 50, Lighting -> "Neutral"]

Yet if I do the same on my Textured ListPlot3D, it doesn't work:

texture = 
  ListDensityPlot[Table[0.5, {y, 0, 50}, {x, 0, 50}], Mesh -> None, 
   InterpolationOrder -> 0, Frame -> False, PlotRangePadding -> None, 
   ImagePadding -> None, ColorFunction -> (Blend[{Blue, Red}, #] &), 
   ColorFunctionScaling -> False];

(* too dark *)
ListPlot3D[Table[p[x, y], {y, 0, 50}, {x, 0, 50}], 
 DataRange -> {{0, 50}, {0, 50}}, PlotStyle -> Texture[texture], 
 TextureCoordinateFunction -> ({#1, #2} &), 
 TextureCoordinateScaling -> True, PlotStyle -> cf[0.5], 
 ViewPoint -> {-1.8, -2.2, 1}, 
 AxesEdge -> {{-1, -1}, {-1, -1}, {-1, 1}}, PlotRange -> {0, All}, 
 MeshFunctions -> (Sqrt[#3] &), Mesh -> 50, Lighting -> "Neutral"]

I tried Glow as in this answer but it wasn't looking great.

Any way to mix Texture and Lighting?

Answer 1

Use Lighting -> "Neutral" as a styling directive in PlotStyle:

ListPlot3D[Table[p[x, y], {y, 0, 50}, {x, 0, 50}], 
 DataRange -> {{0, 50}, {0, 50}}, 
 PlotStyle -> Directive[Lighting -> "Neutral", Texture[texture]], 
 TextureCoordinateFunction -> ({#1, #2} &), 
 TextureCoordinateScaling -> True, ViewPoint -> {-1.8, -2.2, 1}, 
 AxesEdge -> {{-1, -1}, {-1, -1}, {-1, 1}}, PlotRange -> {0, All}, 
 MeshFunctions -> (Sqrt[#3] &), Mesh -> 50]

Answer 2

EDIT

Using ListPlot3D:

So I modified the texture that was a purple sheet mostly.

texture = 
 ListDensityPlot[
  Table[0.5 Sin[0.25 x] Cos[0.25 y], {y, 0, 50}, {x, 0, 50}], 
  Mesh -> None, InterpolationOrder -> 0, Frame -> False, 
  PlotRangePadding -> None, ImagePadding -> None, 
  ColorFunction -> (Blend[{Blue, Red, White}, #] &), 
  ColorFunctionScaling -> True]

and applied it:

ListPlot3D[Table[p[x, y], {y, 0, 50}, {x, 0, 50}], 
 DataRange -> Automatic, PlotStyle -> Texture[texture], 
 TextureCoordinateFunction -> ({#1, #2} &), 
 TextureCoordinateScaling -> True, ViewPoint -> {-1.8, -2.2, 1}, 
 AxesEdge -> {{-1, -1}, {-1, -1}, {-1, 1}}
 , PlotRange -> {0, All}
 , MeshFunctions -> (#3 &)
 , Mesh -> 1
 , Lighting -> "Neutral"
 , ImageSize -> Medium
 ]

---

Original answer

Not exactly ListPlot3D but close:

ListSurfacePlot3D[
 Flatten[#, 1] &@Table[{x, y, p[x, y]}, {y, 0, 50}, {x, 0, 50}], 
 Mesh -> None, MaxPlotPoints -> 50, 
 TextureCoordinateFunction -> ({#1, #2} &), 
 TextureCoordinateScaling -> True,
 AxesEdge -> {{-1, -1}, {-1, -1}, {-1, 1}}, PlotRange -> {0, All}, 
 PlotStyle -> Texture[ExampleData[{"ColorTexture", "CheetahFur"}]]
 , BoxRatios -> {1, 1, 0.3}
 , ImageSize -> Large
 , Lighting -> "Neutral"
 ]