JSFiddle - React, Tailwind, and code Playground

HTML

<h2>Lamp 1</h2>
<span class="ui-li-aside">
    <select id="flip1" data-role="flipswitch">
        <option value="0">aus</option>
        <option value="1">an</option>
    </select>
</span>

<h2>Lamp 2</h2>
<span class="ui-li-aside">
    <select id="flip2" data-role="flipswitch">
        <option value="0">aus</option>
        <option value="1">an</option>
    </select>
</span>

<h2>Both</h2>
<span class="ui-li-aside">
    <select id="flip3" data-role="flipswitch">
        <option value="0">aus</option>
        <option value="1">an</option>
    </select>
</span>

JavaScript

$( "#flip1").change(function(){
    var value1 = $("#flip1").val();
    var value2 = $("#flip2").val();
    
    if (value1 == 1) {
        if (value2 == 1){
            $("#flip3").val("1").flipswitch("refresh");
        }
    }else{
        // should be refreshed cause not both lamps are on status on, but should not refrssh the state of other buttons!
        $("#flip3").val("0").flipswitch("refresh");
    };
});

$( "#flip2").change(function(){
    var value1 = $("#flip1").val();
    var value2 = $("#flip2").val();

    if (value2 == 1) {
        if (value1 == 1){
            $("#flip3").val("1").flipswitch("refresh");
        }
    }else{
        // should be refreshed cause not both lamps are on status on, but should not refrssh the state of other buttons!
        $("#flip3").val("0").flipswitch("refresh");
    };
});

$( "#flip3").change(function(){
    var value3 = $("#flip3").val();
     var value1 = $("#flip1").val();
     var value2 = $("#flip2").val();
    console.log(value1);
    if (value3 == 1) {
        $("#flip1").val("1").flipswitch("refresh");
        $("#flip2").val("1").flipswitch("refresh"); 
    }else{
        if(value1 === 1){            
            $("#flip2").val("0").flipswitch("refresh");
        }
        else if(value2 === 1){
            $("#flip1").val("0").flipswitch("refresh");
        }
        else if(value2 === "1" && value1 === "1"){
            $("#flip1").val("0").flipswitch("refresh");
            $("#flip2").val("0").flipswitch("refresh");                    
        }
    };
});