How do I create a multi-select lookup in D365FO?

A common X++ option is SysLookupMultiSelectCtrl.

SysLookupMultiSelectCtrl multiSelectCtrl;

multiSelectCtrl =
    SysLookupMultiSelectCtrl::constructWithQuery(
        element,
        YourStringControl,
        query);

Keep the controller as a form/class member if you need the selected values later. If you create it as a local variable and then throw the reference away, you make the rest of the form harder than it needs to be.