You can add the native dll as a linked item, and use "Copy if newer".
The problem with native dlls, is that sometimes you'll want to use different dlls according to the project's configuration (Debug/Release or platform).
You can edit the project's .csproj and link the native dll conditionally:
<ItemGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|Win32' ">
<Content Include="..\..\..\..\..\bin\Win32\Release\fanndoubleMT.dll">
<CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
</Content>
</ItemGroup>
<ItemGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|Win32' ">
<Content Include="..\..\..\..\..\bin\Win32\Debug\fanndoubleMT_d.dll">
<CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
</Content>
</ItemGroup>
<ItemGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|x64' ">
<Content Include="..\..\..\..\..\bin\x64\Debug\fanndoubleMT_d.dll">
<CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
</Content>
</ItemGroup>
<ItemGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|x64' ">
<Content Include="..\..\..\..\..\bin\x64\Release\fanndoubleMT.dll">
<CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
</Content>
</ItemGroup>
Note the copy option is set to PreserveNewest which means "copy if newer".