For LW use the proper shader paths that get exported from the LW package..

MaterialGraphProject/Assets/UnityShaderEditor/Editor/Data/Util/GraphUtil.cs

 
                 finalBuilder.AppendLine(@"HLSLINCLUDE");
                 finalBuilder.AppendLine("#define USE_LEGACY_UNITY_MATRIX_VARIABLES");
-                finalBuilder.AppendLine(@"#include ""ShaderLibrary/Common.hlsl""");
-                finalBuilder.AppendLine(@"#include ""ShaderLibrary/Packing.hlsl""");
-                finalBuilder.AppendLine(@"#include ""ShaderLibrary/Color.hlsl""");
+                finalBuilder.AppendLine(@"#include ""CoreRP/ShaderLibrary/Common.hlsl""");
+                finalBuilder.AppendLine(@"#include ""CoreRP/ShaderLibrary/Packing.hlsl""");
+                finalBuilder.AppendLine(@"#include ""CoreRP/ShaderLibrary/Color.hlsl""");
                 finalBuilder.AppendLine(@"#include ""ShaderGraphLibrary/Functions.hlsl""");
                 finalBuilder.AppendLine(@"#include ""ShaderGraphLibrary/ShaderVariables.hlsl""");
                 finalBuilder.AppendLine(@"#include ""ShaderGraphLibrary/ShaderVariablesFunctions.hlsl""");

MaterialGraphProject/Assets/UnityShaderEditor/Editor/DefaultShaderIncludes.cs

         {
             return new[]
             {
-                Path.GetFullPath("Packages/com.unity.render-pipelines.core"),
-                Path.GetFullPath("Packages/com.unity.render-pipelines.lightweight/Shaders"),
-                Path.GetFullPath("Packages/com.unity.render-pipelines.high-quality/Material/Unlit"),
-                Path.GetFullPath("Assets/UnityShaderEditor/Editor"),
-                Path.GetFullPath("Packages/com.unity.shadergraph/Editor"),
+                Path.GetFullPath("Assets/UnityShaderEditor"),
+                Path.GetFullPath("Packages/com.unity.shadergraph"),
             };
         }
     }

MaterialGraphProject/Assets/UnityShaderEditor/Editor/Templates/lightweightPBRExtraPasses.template

-       Pass
+        Pass
         {
             Tags{"LightMode" = "ShadowCaster"}
 
             #pragma vertex ShadowPassVertex
             #pragma fragment ShadowPassFragment
 
-            #include "LightweightPassShadow.hlsl"
+            #include "LWRP/Shaders/LightweightPassShadow.hlsl"
             ENDHLSL
         }
 
             #pragma vertex vert
             #pragma fragment frag
 
-            #include "LightweightShaderLibrary/Core.hlsl"
+            #include "LWRP/Shaders/LightweightShaderLibrary/Core.hlsl"
 
             float4 vert(float4 pos : POSITION) : SV_POSITION
             {
 
             #pragma shader_feature _SPECGLOSSMAP
 
-            #include "LightweightPassMeta.hlsl"
+            #include "LWRP/Shaders/LightweightPassMeta.hlsl"
-        }
+        }

MaterialGraphProject/Assets/UnityShaderEditor/Editor/Templates/lightweightPBRForwardPass.template

     #pragma prefer_hlslcc gles
 	#pragma target 3.0
 
+    // -------------------------------------
+    // Lightweight Pipeline keywords
+    // We have no good approach exposed to skip shader variants, e.g, ideally we would like to skip _CASCADE for all puctual lights
+    // Lightweight combines light classification and shadows keywords to reduce shader variants.
+    // Lightweight shader library declares defines based on these keywords to avoid having to check them in the shaders
+    // Core.hlsl defines _MAIN_LIGHT_DIRECTIONAL and _MAIN_LIGHT_SPOT (point lights can't be main light)
+    // Shadow.hlsl defines _SHADOWS_ENABLED, _SHADOWS_SOFT, _SHADOWS_CASCADE, _SHADOWS_PERSPECTIVE
+    #pragma multi_compile _ _MAIN_LIGHT_DIRECTIONAL_SHADOW _MAIN_LIGHT_DIRECTIONAL_SHADOW_CASCADE _MAIN_LIGHT_DIRECTIONAL_SHADOW_SOFT _MAIN_LIGHT_DIRECTIONAL_SHADOW_CASCADE_SOFT _MAIN_LIGHT_SPOT_SHADOW _MAIN_LIGHT_SPOT_SHADOW_SOFT
-    #pragma multi_compile _MAIN_DIRECTIONAL_LIGHT _MAIN_SPOT_LIGHT
+    #pragma multi_compile _ _VERTEX_LIGHTS
+
+    // -------------------------------------
+    // Unity defined keywords
-    #pragma multi_compile _ _HARD_SHADOWS _SOFT_SHADOWS _HARD_SHADOWS_CASCADES _SOFT_SHADOWS_CASCADES
-    #pragma multi_compile _ _VERTEX_LIGHTS
-
     #pragma multi_compile_fog
 
     #pragma vertex vert
 
-	#include "LightweightShaderLibrary/Core.hlsl"
-	#include "LightweightShaderLibrary/Lighting.hlsl"
-	#include "ShaderLibrary/Color.hlsl"
+	#include "LWRP/Shaders/LightweightShaderLibrary/Core.hlsl"
+	#include "LWRP/Shaders/LightweightShaderLibrary/Lighting.hlsl"
+	#include "CoreRP/ShaderLibrary/Color.hlsl"
 	#include "ShaderGraphLibrary/Functions.hlsl"
 
 	${Graph}
 	    half3 vertexLight = VertexLighting(lwWorldPos, lwWNormal);
 	    half fogFactor = ComputeFogFactor(clipPos.z);
 	    o.fogFactorAndVertexLight = half4(fogFactor, vertexLight);
-
 	    o.clipPos = clipPos;
 
 		return o;
 		float AlphaClipThreshold = 0;
 
         ${SurfaceOutputRemap}
-
-#if defined(UNITY_COLORSPACE_GAMMA)
-       	Albedo = Albedo * Albedo;
-       	Emission = Emission * Emission;
-#endif
 
 #if _NORMALMAP
     half3 normalWS = TangentToWorldNormal(Normal, WorldSpaceTangent, WorldSpaceBiTangent, WorldSpaceNormal);

MaterialGraphProject/UnityPackageManager/manifest.json

 {
 	"registry": "https://staging-packages.unity.com",
 	"dependencies": {
-		"com.unity.render-pipelines.lightweight" : "0.1.22"
+		"com.unity.render-pipelines.lightweight" : "0.1.23"
 	}
 }

MaterialGraphProject/Assets/UnityShaderEditor/Editor/SerializableGraph.meta

-fileFormatVersion: 2
-guid: e47723110397ff04388ed94332cd6208
-folderAsset: yes
-DefaultImporter:
-  externalObjects: {}
-  userData: 
-  assetBundleName: 
-  assetBundleVariant: