Don't normalize the normal coming from the normal map if there's no scaling possible in the shader.

ScriptableRenderPipeline/Core/CoreRP/ShaderLibrary/Packing.hlsl

     return normalize(normal);
 }
 
+real3 UnpackNormalRGBNoScale(real4 packedNormal)
+{
+    return packedNormal.rgb * 2.0 - 1.0;
+}
+
 real3 UnpackNormalAG(real4 packedNormal, real scale = 1.0)
 {
     real3 normal;

ScriptableRenderPipeline/LightweightPipeline/LWRP/ShaderLibrary/Core.hlsl

 
 half3 UnpackNormal(half4 packedNormal)
 {
-    // Compiler will optimize the scale away
-    return UnpackNormalRGB(packedNormal, 1.0);
+    return UnpackNormalRGBNoScale(packedNormal);
+        // Compiler will optimize the scale away
     return UnpackNormalmapRGorAG(packedNormal, 1.0);
 #endif
 }

ScriptableRenderPipeline/LightweightPipeline/LWRP/ShaderLibrary/InputSurface.hlsl

 half3 Normal(float2 uv)
 {
 #if _NORMALMAP
-    return UnpackNormalScale(SAMPLE_TEXTURE2D(_BumpMap, sampler_BumpMap, uv), _BumpScale);
+    #if BUMP_SCALE_NOT_SUPPORTED
+        return UnpackNormal(SAMPLE_TEXTURE2D(_BumpMap, sampler_BumpMap, uv));
+    #else
+        return UnpackNormalScale(SAMPLE_TEXTURE2D(_BumpMap, sampler_BumpMap, uv), _BumpScale);
+    #endif
 #else
     return half3(0.0h, 0.0h, 1.0h);
 #endif

ScriptableRenderPipeline/LightweightPipeline/LWRP/Shaders/LightweightStandardSimpleLighting.shader

 
             #pragma vertex LitPassVertex
             #pragma fragment LitPassFragmentSimple
+            #define BUMP_SCALE_NOT_SUPPORTED 1
             #include "LWRP/ShaderLibrary/LightweightPassLit.hlsl"
             ENDHLSL
         }
             #pragma vertex ShadowPassVertex
             #pragma fragment LitPassFragmentSimpleNull
 
+            #define BUMP_SCALE_NOT_SUPPORTED 1
             #include "LWRP/ShaderLibrary/LightweightPassShadow.hlsl"
             ENDHLSL
         }
             #pragma vertex LitPassVertex
             #pragma fragment LitPassFragmentSimpleNull
         
+            #define BUMP_SCALE_NOT_SUPPORTED 1
             #include "LWRP/ShaderLibrary/LightweightPassLit.hlsl"
             ENDHLSL
         }