As a workaround, we can use jQuery with REST API to achieve it. Use a single line of text field to instead of lookup field, and using REST API and jQuery to get all the Employee Names from List A, and hide this text field add a drop down control in the list form. The following example for your reference.
1.Create a custom list "List A", and create a user field "Employee Name".
2.Create a custom list "List B", and create a single line of text field "Employee Name".
3.Add the following code into a script editor web part into New/Edit form page in List B.
<script src="https://code.jquery.com/jquery-1.12.4.min.js" type="text/javascript"></script>
<script type="text/javascript">
$(function(){
var listId="6C9991B2-50A4-4755-9E4B-9D391C2774FE";
var employeeName=$("input[title^='Employee Name']").val();
$("input[title^='Employee Name']").hide();
$("input[title^='Employee Name']").after("<select id='EmployeeField' class='ms-RadioText'><option value=''></option></select>");
var allEmployeeNames=getAllEmployeeNames(listId);
$.each(allEmployeeNames,function(i,employee){
if(employeeName==employee.Employee_x0020_Name.Title){
$("#EmployeeField").append("<option selected='selected' value='"+employee.Employee_x0020_Name.Title+"'>"+employee.Employee_x0020_Name.Title+"</option>");
}else{
$("#EmployeeField").append("<option value='"+employee.Employee_x0020_Name.Title+"'>"+employee.Employee_x0020_Name.Title+"</option>");
}
});
$("#EmployeeField").change(function(){
$("input[title^='Employee Name']").val($(this).val());
});
})
function getAllEmployeeNames(listId){
var results;
$.ajax({
url: _spPageContextInfo.siteAbsoluteUrl + "/_api/web/lists(guid'"+listId+"')/items?$select=Employee_x0020_Name/Title&$expand=Employee_x0020_Name/Id",
type: "GET",
async:false,
headers: {
"Accept": "application/json;odata=verbose",
},
success: function (data) {
if(data.d.results.length>0){
results=data.d.results;
}
},
error: function (data) {
//alert("Error");
}
});
return results;
}
</script>