Edit: Thanks to a lot of help in the chat from LuisW I now have a working greyscale shader, I didnt have to change anything about my GreyscalePixelShader but I did have to remove the second pass of the simple techique and put it into a seperate technique, as such:

technique Greyscale
{
    pass Pass0
    {
        PixelShader = compile ps_2_0 GrayscalePixelShader();
    }
}

I also had to update my XNA/C# Draw method to create a fullscreen quad that I rendered my scene with the first technique to so I could use my greyscale technique on that quad as an input. Mind you, the method Im using, with spritebatch, is known to be slow (for me that didnt matter, but if you need fast, then drawing the quad directly is supposably faster) My updated draw method:

protected override void Draw(GameTime gameTime)
{
    this.device.Clear(ClearOptions.Target | ClearOptions.DepthBuffer, Color.DeepSkyBlue, 1.0f, 0);

    PresentationParameters pp = this.device.PresentationParameters;
    RenderTarget2D renderTarget;
    renderTarget = new RenderTarget2D(this.device, pp.BackBufferWidth, pp.BackBufferHeight, true, pp.BackBufferFormat, pp.DepthStencilFormat);
    this.device.SetRenderTarget(renderTarget);
    this.device.Clear(ClearOptions.Target | ClearOptions.DepthBuffer, Color.DeepSkyBlue, 1.0f, 0);
    Rectangle screenRectangle = new Rectangle(0, 0, screenWidth, screenHeight);

    // Get the model's only mesh
    ModelMesh mesh = this.model.Meshes[0];
    Effect effect = mesh.Effects[0];

    effect.CurrentTechnique = effect.Techniques["Simple"];

    //<left out some noninteresting worldmatrix calculations here not relevent for this question/answer> 

    device.DepthStencilState = DepthStencilState.Default;
    device.BlendState = BlendState.Opaque;

    mesh.Draw();

    this.device.SetRenderTarget(null);

    effect.CurrentTechnique = effect.Techniques["Greyscale"];

    spriteBatch.Begin(0, BlendState.Opaque, null, null, null, effect);
    spriteBatch.Draw((Texture2D)renderTarget, screenRectangle, Color.White);
    spriteBatch.End();

    base.Draw(gameTime);
}

The following code gives me a completely black colored model, while it should be a model shaded in greyscale:

float4 SimplePixelShader(VertexShaderOutput input) : COLOR0 { //some lambertian shading done in the code I left out here

return color;

}

sampler TextureSampler = sampler_state { Texture = ; };

float4 GrayscalePixelShader(float2 TextureCoordinate : TEXCOORD0) : COLOR0 { // Get the color. float4 color = tex2D(TextureSampler, TextureCoordinate);

// Turn pixel to grayscale.
float grayscale = dot(color.rgb, float3(0.3, 0.59, 0.11));
color.r = grayscale;
color.g = grayscale;
color.b = grayscale;
color.a = 1.0f;

// Return the result.
return color;

}

technique Simple {

pass Pass0
{
    VertexShader = compile vs_2_0 SimpleVertexShader();
    PixelShader  = compile ps_2_0 SimplePixelShader();
}

pass Pass1
{
    PixelShader  = compile ps_2_0 GrayscalePixelShader();
}

}

As far as I could find out the problem lies here: // Get the color. float4 color = tex2D(TextureSampler, TextureCoordinate);

the whole lambertian coloring works, the grayscale seems to work properly by itself after some testing, but what doesnt seem to work is getting the red lambertian shaded model colors. Anybody any clue what Im doing wrong?

The following code gives me a completely black colored model, while it should be a model shaded in greyscale:

float4 SimplePixelShader(VertexShaderOutput input) : COLOR0
{
    //some lambertian shading done in the code I left out here
    
    return color;
}

sampler TextureSampler = sampler_state
{
    Texture = <ScreenTexture>;
};

float4 GrayscalePixelShader(float2 TextureCoordinate : TEXCOORD0) : COLOR0
{
    // Get the color.
    float4 color = tex2D(TextureSampler, TextureCoordinate); 
    
    // Turn pixel to grayscale.
    float grayscale = dot(color.rgb, float3(0.3, 0.59, 0.11));
    color.r = grayscale;
    color.g = grayscale;
    color.b = grayscale;
    color.a = 1.0f;
    
    // Return the result.
    return color;
}

technique Simple
{

    pass Pass0
    {
        VertexShader = compile vs_2_0 SimpleVertexShader();
        PixelShader  = compile ps_2_0 SimplePixelShader();
    }
    
    pass Pass1
    {
        PixelShader  = compile ps_2_0 GrayscalePixelShader();
    }
}

As far as I could find out the problem lies here:

// Get the color.
float4 color = tex2D(TextureSampler, TextureCoordinate);

The whole lambertian coloring works, the grayscale seems to work properly by itself after some testing, but what doesnt seem to work is getting the red lambertian shaded model colors. Anybody any clue what I'm doing wrong?