How can i get the value from a in my Controller Laravel 6.0

Im trying to save the value from a select that has the id's from tables in sql, but i dont know how to get the value from the select in my controller, i want to put my foreign key= the value of the select , the type of the value in the select is integer

-Below i will let the code of my select and the code of my store function()

• id_lugaris the information that i show

• I tried this $cliente_natural->fk_lugar=$('#municipio').val(); but doesnt work

Select code

<div class="form-group row">
                <label for="lugar" class="col-md-5 col-form-label text-md-right">Estado</label>

                <div class="col-md-6">
                    <select id="estado" name="id_lugar" class="form-control{{ $errors->has('id_lugar') ? ' is-invalid' : '' }}">
                        @foreach($lugares->get() as $index => $lugar)
                            <option value="{{ $index }}" {{ old('id_lugar') == $index ? 'selected' : '' }}>
                                {{ $lugar }}
                            </option>
                        @endforeach
                    </select>

                    @if ($errors->has('id_lugar'))
                        <span class="invalid-feedback" role="alert">
                            <strong>{{ $errors->first('id_lugar') }}</strong>
                        </span>
                    @endif
                </div>
              </div>

              <div class="form-group row">
                <label for="lugar" class="col-md-5 col-form-label text-md-right">Municipio</label>

                <div class="col-md-6">
                    <select id="municipio" data-old="{{ old('id_lugar') }}" name="id_lugar" class="form-control{{ $errors->has('id_lugar') ? ' is-invalid' : '' }}"></select>

                    @if ($errors->has('id_lugar'))
                        <span class="invalid-feedback" role="alert">
                            <strong>{{ $errors->first('id_lugar') }}</strong>
                        </span>
                    @endif
                </div>
              </div>

Store function()

public function store(Request $request)
    {
        $cliente_natural=new Cliente_natural();
        $cliente_natural->primer_nombre=$request->primer_nombre;
        $cliente_natural->segundo_nombre=$request->segundo_nombre;
        $cliente_natural->primer_apellido=$request->primer_apellido;
        $cliente_natural->segundo_apellido=$request->segundo_apellido;
        $cliente_natural->cedula=$request->cedula;
        $cliente_natural->rif=$request->rif;
        $cliente_natural->numero_carnet=$request->numero_carnet;
        $this->validate(request(), [
            'email' => 'required|email',
            'password' => 'required|confirmed|min:8',
        ]);
        //$cliente_natural->email=$request->email;
        //$cliente_natural->password=$request->password;
        $cliente_natural->fk_lugar=$('#municipio').val();


        $cliente_natural->save();
        return view('home.home2');
    }